Neither of these sentences uses parallel structure. Parallelism means that both parts of the sentence have the same, i.e. parallel structure, e.g. if one part of the sentence has a verb in present continuous followed by an adjective and a noun, then the other part of the sentences needs the same. If it doesn't, it is not considered parallel structure. Here is an example:
Parallel structure: I am buying a green hat today, and I am selling a red car tomorrow.
Not parallel: I am buying a green hat today and will probably also sell my car.
As for your sentences, here they are but with parallel structure:
- Not only was she noisy and rude but also stupid and belligerent. (you cannot repeat "she was" in this sentence - "not only ... but also" structure - and you need two adjectives connected with "and" to have a parallel structure)
- The Admiral was told he was either a liar or a fool. (again, you cannot repeat "he was"; here we have two nouns; that's fine)
- The car is not only economical but also beautiful. (two adjectives + shortened "not only ... but also" structure)
