pada: word or morpheme?

I think that pada might mean either `word' or `morpheme', if the latter can be conceived of as having an independent meaning, like in the case of the optative verbal ending.
For the historical background of this double meaning, see the following quote:

For Yāska the Vedic Saṃhitās are made of padas. It is not clear whether this refers to verse-quarters, words or whole verses. Pāṇini restricts the meaning of pada to `word' or word-component. pada may mean here `verb', but also `substantive' or `prefix'.

(``Für Yāska sind die vedischen Saṁhitās aus padas gemacht. Ob es sich hier um Vers-viertel, Worte oder ganze Verse handelt, ist nicht klar. Pāṇini (1.4.14) engt die Bedeutung von pada auf `Wort' oder auch Bestandteile von Worten ein. Pada kann hier sowohl Verb als auch Substantiv, aber auch Präfix bedeuten". (Lars Göhler 2011, p.69).

Transcriptions from Devanagari (etc.) into Roman alphabet

Apart from whimsical transcriptions linked to the prehistory of Sanskrit studies or to their periphery, Sanskrit is usually transcribed in a standard way, e.g.:

pramāṇato 'rthapratipattau pravṛttisāmarthyād arthavat pramāṇam || NS 1.1.1 ||

Interestingly enough, however, transcriptions still widely differ as for the word-boundaries. Personally, I tend to separate as much as possible, since this procedure seems to me reader-friendlier. Other authors, prefer instead to reproduce in the Roman alphabet the scriptum continuum typical of Devanagari and other Indian alphabets. For instance,

What are the advantages of this usage? I can easily imagine some textual-critical advantages:

1. 1. it makes readers aware of the text as it looked like in the manuscript,
2. 2. it avoids influencing readers with the editor's understanding of the text.

However, apart from the case of diplomatic editions, the influence of the editor is explicit, especially so in studies. And why should one make life more difficult to readers?
In many cases, for instance when a neutrum term could be considered as part of a compound or as a nominative/accusative, the difference might be significant. For instance:

arthe 'nupalabdhe tatpramāṇam bādārāyanasya anapekṣatvāt

is quite different than:

arthe 'nupalabdhe tat pramāṇam bādārāyanasya anapekṣatvāt (end of MS 1.1.5)

What do readers think? Are there further reasons for the scriptum continuum also in Roman transcriptions I am missing?

Cicero pro domo sua

I felt personally addressed by an intriguing post by Vidya (here) which asks how could one with little or no knowledge of rituals be able to understand Mīmāṃsā texts.
The post is highly recommendable and raises many interesting points.
Personally, although I have been reading Mīmāṃsā texts for …(too many) years now, not only I lack a lot of the knowledge I should have, but also I am not in the position to acquire it, being a mleccha woman.

Let me first be apologetic: the same problem does not only apply to tantric āgamas (as admitted by Vidya), but also to texts dealing with Medicine, Yoga, Architecture. meditation techniques and any other technical subject (one is reminded of endless discussions about whether a non-Buddhist might understand Buddhist texts). Further, I would say that sharing the authors' worldview (which seems to be Vidya's main point) is fundamental also for philosophical texts. One cannot think of editing or translating Kumārila or Jayanta just through a bunch of manuscripts and one's acquaintance with Sanskrit. One should (I believe) be ready to engage in a philosophical dialogue with them.
This leads me to a further point: Mīmāṃsā authors are not yajñikas (as established by Daya Krishna in his well-known The Mīmāṃsaka and the Yajñika). They do not (or not merely) aim at performing ritual in a correct way, they aim at conceiving the ritual in a correct way. This is evident in thousands of cases where the end-result does not change and yet authors argue at length about which principle should be applied (e.g. MS 12.1.10-11). To disregard this fundamental difference, I believe, is to do violence to the deep philosophical significance of Mīmāṃsā.
Last, a word of caution: Vidya seems to imply that a contemporary yajñika might be in a better position to understand a Mīmāṃsā text. This might be true. Among my favourite Mīmāṃsā scholars are several Indian paṇḍits, such as G. Jhā, P.K. Sen and K. Pandurangi, whom I immensly admire. But knowing how something is done today does not automatically entail knowing how it was made at the time of Śabara. I dedicated several posts in the last months to the history of the terms tantra and prasaṅga and hope to have been able to show how their meaning changed throughout centuries. In short: being aware of philosophy and of philosophy in history seems to me the fundamental precondition for understanding Mīmāṃsā philosophical texts.
Yet, Vidya is right. I argued elsewhere that it is ironic that examples, meant to be clarifications, are often the hardest part of a Mīmāṃsā passage. What should one do? First, work in a team with people who are more acquainted with rituals or with ritual manuals (paddhati). Second, think along the Mīmāṃsā way. "Think ritually", as F.X. Clooney would put it. This implies some revolutions, for instance, thinking in a spatial way rather than in a temporal one.

What is the readers experience in fields where they are outsiders?

On team-work, see here. On thinking spatially, see here (in Śrautasūtras), here (in Śrautasūtras and early Mīmāṃsā), here (in general) and here (on absence as a spatial and not temporal category). On the use of history, see here. With God's help, I will be speaking about how to critically editing a philosophical text during the next WSC.

If something is already in use, you do not need to further justify its use

I am always fascinated by the pragmatic logic of the Mīmāṃsā school (and often of every speculation about ritual). The one hinted at in the title is one of these cases: if something is already in use, it goes without saying that it is correct to use it, and one only needs an epistemic foundation for something one starts using.
prasaṅga occurs three times in MS, all very close to each other, in MS 12.1.10-11 and 15. The context is that of the archetype sacrifice-ectype sacrifice (prakṛti/vikṛti) relationship and of the way elements are analogically translated from the former to the latter.

The first of these three sūtras is traditionally read as a PP, possibly depending on the vā found in the subsequent one:

pātreṣu ca prasaṅgaḥ syād dhomārthatvāt. (10)
nyāyyāni vā prayuktatvād aprayukte prasaṅgaḥ syāt. (11)

A provisional translation could sound like:

[PP:] And, as regards the vessels, [their function] might be automatically entailed (in a subsequent rite), since they are for the sake of the oblation.

[S:] Better: since [they] are [already] in use, they are regularly [to be employed]. The automatic entailment applies [only] in regard to something which is not already in use.

If the attribution to a PP is right, the objector argues that, in regard to the vessels, one might "apply" (i.e., analogically translate) them from the prakṛti, since both vikṛti and prakṛti have a common purpose, i.e., the oblation. The PP is here implementing the instrument of knowledge for deciding what has to be analogically extended called artha, that is, inferring the proper element to be translated from its purpose (rather than out of a specific mention in the text, etc., see MNP 199, 201). The S replies that the vessels are regularly to be employed, since they are in use. This does not seem to confute the preceding sūtra. It accepts the employment of the vessels, but not out of their translation from the prakṛti, rather out of their being already in use. Further conditions (in the present case, prasaṅga) apply only if there is not already something in use.

In other words, the principle of automatic entailment only applies if something is not already in use (and hence does not need any entailment). I am understanding prasaṅga in sūtra 11 as a principle and not a concrete act of entailment because one would not have a reason to repeat that the concrete entailment does not occur.

Do readers know of similar common-sense principles in texts which do not deal with ritual?

On prasaṅga in the Śrautasūtras, see here. On prasaṅga in Mīmāṃsā, see here.

Zero in Indian philosophy

Grammarians and linguists are familiar with the idea of a function of the ‘absence’ of morphemes which is currently called “zero”. Western linguists beginning with de Saussure's work of 1879 have often postulated the existence of the so-called zero-morphemes where the actual perceptible linguistic form does not match its relevant semantic and syntactic content (see T. Pontillo 2002, p.559ff.). They resorted to this device on the basis of a significant opposition pointed out between comparable morphological structures.
As focused by Al-George (Al-George 1967, p.121), on the other hand, the Indian linguistic zero is not a mere device, adopted for a descriptive purpose. It rather seems to represent “the consequence of a definite philosophy of form”, namely “the category which exists though not embodied in a concrete form, suspended as a pure virtuality at the border between existence and non-existence”.

A more general problem is: How can an absent element perform a function notwithstanding its absence? How comes that an effect can be grasped in absence of its cause?

On the latter problem, see here (on tantra and prasaṅga as a possible answer).

Are there general rules in Vedic rituals? No, just material entailments

prasaṅga is not frequent in the Śrautasūtras and I failed to find a definition of it. Hence, one has to reconstruct its meaning indirectly, through its usage in the ŚrSū, through its usage in Grammar and Mīmāṃsā and possibly also through its etymological meaning. Every translation is therefore intrinsically tentative.

In its only occurrence in the Aśvalāyana Śrautasūtra (AśvŚrSū 1.1.22) it is opposed to apavāda (certainly meaning "exception"):

prasaṅgād apavādo balīyaḥ

Mylius translates:

Eine Ausnahme (-Regel) ist gewichtiger als eine allgemeine Regel (Mylius 1994: 29a)

That is, "An exceptional [rule] is more forceful than a general rule".

But the meaning seems, more precisely, to be "default occurrence". The prasaṅga is what one expects to happen, what follows by default from the previous discussion. Only secondarily, it defines the "general" rule. Hence,

An exception is stronger than what is automatically entailed.

On prasaṅga, see here. On the problem of reconstructing the meaning of a term, when the technical context is lost, see here.

Tantra and prasaṅga in a Catholic Mass

During a Mass, the hosts are not severally consecrated. Their consecration is valid once for all. Using the terminology of the Indian ritualistics, one could say that it happens once for all, through tantra. Each host is part of the same rite and hence shares all the benefits of any act performed within the rite.

By contrast, imagine the case of two different rituals, like the Sunday Mass and the special Mass celebrated on the day of the Assumption of the Virgin Mary. Both Masses have to be attended compulsory by Catholic believers, but one can attend any of the Masses celebrated on that day or on the evening before. In other words, one is allowed to attend either one of the Sunday Masses celebrated during the whole Sunday or the "Sunday Mass" celebrated on Saturday evening. What happens if the day of the Assumption occurs on a Saturday (as it happens every seven years)? Is one allowed to go to the Saturday evening Mass and fulfil through the same act both duties? If yes, one could say that the function of the Mass celebrated on the Saturday evening as a "Sunday Mass" helps one fulfilling both duties. It fulfills directly the duty to attend the Sunday Mass and indirectly the duty to attend the Mass on the day of the Assumption of the Virgin Mary. This kind of double effect which was not intended could be called prasaṅga.
However, I am inclined to think that a Catholic believer should go to the Mass twice, once on the day of the Assumption of the Virgin Mary (in the present example, on the Saturday) and once on the Sunday (or on the Saturday evening), because the liturgy has a specific prescription about the fact that one has to attend the first and the second one. And, when there is a specific restriction, prasaṅga cannot apply (prasaṅgād apavādo balīyaḥ or prasaṅgo na, niyamaśabdāt).

On tantra, see here. On prasaṅga, see here.