What does an adjunct modify?

In your example,

He talked about me in a hateful way.

"in a hateful way" modifies the verb phrase "talked about me", and the result of the modification is a verb phrase "talked about me in a hurtful way". All modifiers are like this -- they are added to a phrase of some certain syntactic type, and give as result another phrase of that same type, but with a modified meaning.

We can verify that both "talked about me" in the example and "talked about me in a hateful way" are verb phrases, by using the do-so test proposed by Lakoff and Ross (Criterion for verb phrase constituency). "Do so" is an anaphoric replacement for a verb phrase, and we have:

He talked about me, and then she did so. ("did so" = "talked about me")
He talked about me in a hateful way, and then she did so in a loving way. ("did so" = "talked about me")
He talked about me in a hateful way, and then she did so. ("did so" = "talked about me in a hateful way")

This follows the account of modification in McCawley's The Syntactic Phenomena of English.

So "in a hateful way" is not an adjunct, and it modifies neither a verb or a noun, but rather a verb phrase.

Adjuncts, which are a very broad set of things, can modify any part of speech. I've never heard that adjuncts "always" modify nouns.

Regarding "limitation": You aren't limited by any rule that says "you can only use X number of consecutive adjuncts", but you're limited by practicality. Once you start adding so many, obviously it becomes irritating for the reader to get through. The meaning isn't unclear, exactly, but it's not a fun sentence to read.

Those interpretations aren't different in meaning. The second one is a sillier way of saying it, of course, but the conclusions are the same.