NSM primes do have fixed meanings that don't include all of the polysemy present in a language. For example, the YOU prime is strictly singular, so you might need to be careful not to just use YOU for the English word "you" if your meaning was plural, you'd also have to use one of the quantifier primes.
Primes can be identified in a particular language through a set of "canonical sentences", which is available to download. There isn't a particular canonical sentence that covers speaking to yourself alone in a room, but I don't think it would be considered a different sense than the prime sense of SAY. (Consider the difference between "say" and "tell" in English, where "tell" really requires another person.)
The primes don't cover metaphorical extension. For example, it's very natural to use the word "say" to cover what we type or write to each other. But in NSM you'd have to describe that using the LIKE prime. Or perhaps a lot of the time the actual medium of communication is irrelevant, and you could just use the SAY prime.
The most detailed description of each prime that I'm aware of is in Anna Wierzbicka's 1996 book "Semantics: Primes and Universals". I'm not sure if there's a more recent book that goes into as much detail for every prime, or if the more recent amendments to the list of primes are just discussed case by case. But this book's chapter called "A Survey of Semantic Primitives" is very helpful, giving a detailed explanation of each prime.
The section on SAY is not very long, so I can just quote it all here (page 50):
The universal concept of SAY can be illustrated with the following canonical sentences:
I said something to you.
People say something bad about you.
I want to say something now.
Like the indefinability of mental predicates (e.g. THINK), the indefinability of SAY can best be appreciated by looking at contortions and vicious circles in the attempted dictionary definitions of this word.
The concept of SAY plays an important role in speech as a basis of different illocutionary forces (e.g. in questions which imply: 'I want you you say something'), in the thematic organization of utterances ('I want to say something about this'), and in the basic "subject-predicate" structure of sentences ('I'm thinking about X; I say Y'). In the lexicon, its most important function lies in the categorization of discourse, since the distinctions between different "speech acts" and "speech genres" shape, to a considerable extent, our interpretation of human interaction. (See Wierzbicka 1987a.)
