Are the sentences below grammatically correct?
I didn't support Gheddafi and I will never support him.
I didn't support Gheddafi and will never support him.
I didn't support Gheddafi and never will support him.
There are two different factors at work in the three sentences, all of which feature automatic pronominalization (Gheddafi ==> him) in the second clause.
Sentence 1 is the basic sentence. Two main clauses conjoined with and. Both clauses have first person singular subject (I), and both clauses have verb phrases headed by auxiliary verbs (did and will). This is certainly grammatical.
Sentence 2 is just Sentence 1 after Conjunction Reduction has applied. That process deletes the repeated I subject in the second clause, thus reducing the conjoined clauses to a single clause with a single subject, but a conjoined verb phrase. This is also grammatical. Neither 1 nor 2 is problematic, and there is no meaning difference between them; both occur and individual usage varies.
Sentence 3 is Sentence 2 with a different placement of never. This is where noticing that never is a negative turns out to be useful, since the rule for negative placement says that
So the following are all OK:
because will support him and have supported him are VPs that contain the focussed VP. So never can go either immediately before will/have, or immediately before support(ed). Again, such placement makes no difference in meaning or grammaticality; this is another matter like Conjunction Reduction where individual usage varies.
1- I didn't support Gheddafi and I WILL NEVER support him.
2- I didn't support Gheddafi and WILL NEVER support him.
3- I didn't support Gheddafi and NEVER WILL support him.
1 -I didn't support Ghaddafi and I shall never support him
2 -I didn't support Ghaddafi and shall never support him.
Number two sounds better, though. You have already mentioned it is you who is supporting him. About the replacement for will, shall sounds better, even if it is old fashioned.