Sorry, I've been slacking, I'm not sure what all you guys know, and I can't think straight, so this is rather random blah...
Why do you guys think those "words" that function as auxiliaries should be considered simple? That's the main thing that I'm trying to decide -- whether they're functioning at the morpheme or phrase level. And I need
justifications. (Actually, complex auxiliaries do exist;
be, have, and
do are still inflected for tense and agreement when functioning as auxiliaries, so excepting those cases...) For example, the first thing I need to determine is whether they are words. I think there existing (AFAIK) no syntactic rule that applies to any of their "parts", their being inverted to form questions, and their preceding negation are good reasons to consider them words. I'm not sure whether those reasons are good enough, but I'm willing to just assume for now that they're words.
I next need to decide several things, in whichever order works (and there isn't necessarily a best answer): Is each word simple or complex? Are each of their morphemes free or bound? Lexical or grammatical? If grammatical, are they derivational or inflectional? What does each morpheme mean? Are any of them forms of others? Are the forms regular or irregular? Are there subregularities? And possibly other questions, depending on what the other answers are.
Some problems:
Since they're words, if they're simple, they're free. But the modals, at least, also seem to be inflectional in some cases, and I'm not sure that a morpheme can be both free and inflectional, i.e., whether that makes sense or would cause problems, etc. For instance, the modals (AFAIK) aren't inflected for tense or agreement, but they seem be tensed; so are they themselves the inflectional morphemes?
Is
could (in some environments) the simple past form of
can (in one of its meanings), or is that just a part of the general meaning of
could? Is
will/shall (in one of their meanings) some kind of future tense of
do (in one of its functions)? In which theories does English have a future tense? Why / why not? And so on.
Modals have non-modal interpretations. Primaries,
will,
need, and possibly others are also main verbs.
do is just extra weird.
Semi-auxiliary phrases.
Blah. Sorry.

It just keeps getting complicated so quickly that my progress is incredibly slow, and I feel as though I'm missing something important (that would make it all simple).