Welcome to the Grammar Exchange, NPEXP (does that stand for "noun phrase expert," by any chance? )
I'll give you my view:
Is 'so much about languages I would like to understand' a noun phrase?
To me, it is a noun phrase, with "much" being a pronoun, similar to "a lot." Actually, "there + be" needs to be followed by a nominal construction.
Is 'more than five months' a noun phrase (as part of a prepositional phrase?)
I think you are right: "more than five months" is the object to the preposition "for." In my opinion, "months" is the head and "more than five," a premodifier.
Is 'my sister playing the piano all the time' a NP or a non-finite adverbial clause?
That is an absolute construction functioning as a non-finite adverbial clause, with a subject ("my sister") and a predicate ("playing the piano all the time").