Are the following sentences gramatically correct?:
Nokia is not your favourite brand but is the best in my opinion
where "it" has been dropped, and
They regulate neuronal response, but are incapable of performing other actions
where "they" has been dropped.
The first one doesn't sound good to me, but can`t explain why.
Is the comma somehow important when it comes repeting the subject?
In the first example, the comma feels necessary because you're connecting two independent clauses, not because you're repeating the subject.
The two clauses, "Nokia is not your favorite brand" and "it is the best in my opinion," both can stand alone grammatically as simple sentences. This is what makes them independent clauses.
In school, I learned the "comma FANBOY rule" (For And Nor But OR Yet), it's the first comma rule in this guide:
Use commas to separate independent clauses when they are joined by any of these seven coordinating conjunctions: and, but, for, or, nor, so, yet.
The game was over, but the crowd refused to leave.
The student explained her question, yet the instructor still didn't seem to understand.
https://owl.english.purdue.edu/owl/resource/607/02/
However, when the two clauses are well balanced, I'd say it's pretty common and widely accepted to leave this comma out. Because of this, I've heard someone call the FANBOY rule a pseudorule.
In your first example, the two phrases aren't well balanced in my opinion. The word is without a subject feels really jarring, even though it is grammatically equivalent to the word are in your second example.
"Nokia is not your favourite brand, but the best in my opinion"
This is how I would re-phrase it. "is" needn't be repeated, as we're still talking about 'Nokia'.
As for your second sentence, I find it correct.
