One problem is that the entire concept of "part of speech" is very old. How we use it in English, especially in dictionaries, goes back to the study of Latin and Greek. In this view of English grammar "adverb" is the catch-all category where everything that doesn't fit into one of the other traditional categories ends up. (The others being noun, verb, adjective, pronoun, preposition, conjunction, and interjection.)
Now there is no one, true description of any language (except perhaps constructed languages such as yours). There are merely alternative or competing descriptions which appear over time as more independent analyses of the language are undertaken. Such descriptions or analyses may be called "grammars".
Most (but not all) grammars include a concept of word class under one name or another. So one problem is that "part of speech" has two meanings. One is the specific set of eight categories from the classical languages, the other is as a synonym for word class, which is a lot looser.
So all your example words are adverbs under this older stricter view of parts-of-speech, but their qualities and quirks can be much more thoroughly investigated in newer ways. And various new ways will have various new terms for the classes they put these various words into.
Unless you are inventing a new language specifically to embrace the classical parts of speech you don't have to worry in which they belong, but if you are inventing a new language to learn more about how language works then it will be worth your time reading up on the many newer grammars and language descriptions and analyses.
Best Answer
The linguistic or grammatical principle that likely provokes your concern is termed coordination. Here's Wikipedia's article on the subject.
There often needs to be some kind of match between the elements that are coordinated in a sentence. But many of us poorly understand which kinds of matches and mismatches are grammatically felicitous, questionable, or generally unacceptable. In fact, it's a challenge for linguists to specify a parsimonious set of rules governing this matter.
Linguists often use the following as an example of elements which are mismatched in terms of sentence part categories, but permitted because they match in terms of function:
A Republican is a noun phrase, while proud of it is an adjective phrase.
We might therefore wonder if setting them in coordination is permissible. It is, in this case, because although they do not match in terms of sentence part category, they do match in terms of function: They both complete (complement) the subject.
Your example does the same thing. The prepositional phrase and the adjective phrase both complement the subject, and they match in a way such that they can be acceptably set in coordination.
This doesn't mean that all complements can be cast as coordinates. As alluded to above, useful guidelines on this are hard to come by.
Whether or not your example is good or bad style is more subjective. If people who are good talkers were to debate it, surely they would want to know whether it was to be spoken or written, in which sort of genre, and targeted toward which kind of listener or reader. In and of itself, there is nothing bad about the style. Its meaning is clear. To me.
You have confused parts of speech with sentence constituents. A part of speech is a label attached to a lexeme or "word", like adjective, preposition, or noun. A sentence constituent is a label attached to a meaningful part of a sentence which can be characterized as playing a functional role in the sentence's structure, like subject, complement, or object.
There are situations in which elements in a set need to agree in some way, some situations in which it's better style if they do, and some situations which are generally seen as bad style, ungrammatical or just nonsensical if they are divergent.
Fine:
The items in this "enumeration" or set of elements would be considered bad style by most:
Ungrammatical or nonsensical (?):
NOTE: Thanks to @snailboat for redirecting my original answer onto firmer linguistic ground insofar as identifying the relevant topic. She deserves credit for what I got right, and no fault for the answer's travels into Errorsville, Papland or Drivelvania.