I think the best way to answer your question is to provide simple grammatical rules in using all coordinating conjunctions (your two examples above list two, "and" and "but") in making two simple sentences wherein the subject is the same in both, the verb in both sentences become parallel verbs, and the subject (Either name or pronoun) does not need to be repeated. Consequently, if the verb as well is the same in both simple sentences where the subject is also the same, the verb as well does not need to be repeated. It can be for emphasis, but is not necessary.
Example: I eat cupcakes. I don't eat bread.
Since the subject ("I") in both of these simple sentences is the same, it's not necessary to repeat "I" (a pronoun). Additionally, since the verb in both simple sentences is the same, it's not necessary to repeat that, either. Both these sentences can be connected into a compound sentence with a coordinating conjunction. It's important to note conjunctions and, but, nor, and or always connect words or word groups of the same kind--that is two or more nouns, verbs, adjectives, adverbs, phrases, subordinate clauses or main clauses, and in the example above both subject and verb are the same, so use "and" "but" "nor" or "or" to connect them.
I eat cupcakes. I don't eat bread. becomes, I eat cupcakes, but not bread.
Why? Again, both subject and verb are the same in both sentences and don't need to be repeated when connected with a coordinating conjunction. I can say, "I eat cupcakes, but I don't eat bread." if I adamantly want to stress emphasis; but, it's not necessary.
Since "and" is also a coordinating conjunction like "but" in that it always connects words or word groups of the same kind (two or more nouns, verbs, adjectives, adverbs, phrases, subordinate clauses, or main clauses) to connect two simple sentences together, here's an example with "and" used:
I sometimes sleep on the couch. I sometimes sleep on my bed.
Since in both simple sentences, the subject, adverb, and verb are the same, it's not necessary to repeat any of them when the sentences are connected with the coordinating conjunction "and."
I sometimes sleep on the couch. I sometimes sleep on my bed. becomes
I sometimes sleep on the couch, and on my bed.
Again, though I can (yes, can!) any or all of them for emphasis, if I want to.
I could say, "I sometimes sleep on the couch, and sometimes sleep on my bed." or, I sometimes sleep on the couch, and sometimes on my bed." I simply repeat what I want for emphasis.
So, to answer your question, all examples 1A & 1B, to 2A, 2B, 2C - are all correct.
The most natural native speaker level sounding is 1A, and 2C, because both follow the rules for coordinating conjunctions. However, any or all are correct as they provide emphasis; albiet, many readers or listeners would think the emphasis is unnecessary.
Many .edu college libraries use the acronym "FANBOYS" (For, And, Nor, But, Or, Yet, So) Ref: Little Brown Handbook, 10th Ed., Pg. 257, Pearson Education, Inc (2010). See below.
It's important to grasp some coordinating conjunctions pair with other words and become correlative conjunctions. Some of the common ones are, "both...and" "not only...but" "either...or" "neither...nor" "as...as" - and is crucial to grasp the proper useage of common correlative conjunctions and their rules for use as well.
Below is downloaded from Michigan State University Online Reading Lab IRT "FANBOYS"
Compound Sentences with Coordinating Conjunctions (FANBOYS)
A compound sentence contains two separate subject and verb pairs. You can combine two simple sentences together with a comma and a coordinating conjunction to make one compound sentence. Here are some examples:
F – for I drank some water, for I was thirsty.
She put on a sweater, for it was cold outside.
*for means the exact same thing as because. The only difference is that when you use for to join two sentences together into one compound sentence, you need to use a comma before it. When you use because to join to sentences, you don’t use a comma before it.
A – and He was tired, and he had a headache.
N – nor She doesn’t drink milk, nor does she eat butter.
I can’t whistle, nor can I sing.
He didn’t study last night, nor did he read his book.
They were not wearing jackets, nor were they carrying umbrellas.
*nor means “also not”. Nor requires unusual grammar. The first sentence will contain a negative verb. The second sentence will contain what looks like an interrogative affirmative verb form. An auxiliary verb (do/does/did, is/am/are/was/were), modal verb (can/could/will/would/may/might/must/should), or be main verb (is/am/are/was/were) comes after nor and before the subject, and then the main verb comes after the subject.
B – but Tom studied a lot, but he didn’t pass the test.
O – or He can buy the book, or he can borrow it from the library.
Y – yet Tom studied a lot, yet he didn’t pass the test.
*yet means the same thing as but.
S – so Maria was thirsty, so she drank some water.
It was cold outside, so she put on a sweater.
