(1)
I don't care too much about it.
In this sentence, 'much' is a 'pronoun' or an 'adverb'?
(2)
A situation or action is too much for you
In this sentence, 'much' is a 'pronoun' or an 'adjective'?
I don't care too much about it.
Too much answers the question "how X do I care?" "How" questions are adverbs (they qualify the sense of a verb).
A situation or action is too much for you
Much is a pronoun here. To be is a copular verb that can act as an "equal sign" for two nouns. Pronouns are able to take the place of nouns or stand in for where a noun would go but doesn't appear because the idea is indefinite.
Much is never an adjective. If you want to say there's a large amount of X, and X is a noun, use many instead.
There was much disappointment today.
There were many disappointing events today.
You're right, much can be a determiner. Most determiners that don't also act as pronouns are never on the far end of a copular verb. For possessive pronouns (really determiners), there's special words for example.
This is my box.
This box is mine (if you said this box is my the listener/speaker will think the sentence is unfinished).
But if the determiner can also be a pronoun, then it's fine to put it after to be or other copular verb.
My box is this (works because this works as a determiner and pronoun).
There is much chaos.
The chaos is much.
It's far more common to use a qualifier like too or very with much after to be or other copular verb, but a plain much isn't wrong. It will sound a little jarring and is less common than using a qualifier with much.
The chaos is too much.
It seems a bit much.
The perfume doesn't smell very much.