About the word order. Would "Han talar inte engelska heller" be grammatically fine?
Yes, that also works. Which one is used often depends on the context and what the speaker wants to emphasise etc.
I'll give it a shot, I think Han talar inte heller engelska means 'Just like (somebody else), he does not speak English', and Han talar inte engelska heller means 'Just like he does not speak (another language), he does not speak English either'. Something like that.
Nope, you can't (unless you're writing poetry or lyrics or something).
What you could say, but which sounds a bit poetic and stilted, is "Inte heller han talar engelska.". This is specifically the kind of heller which means that there's also another person not speaking English.
On the other hand, "Inte talar han heller engelska." (there's another person) or "Inte talar han engelska heller." (there's another language he doesn't speak) are perfectly fine. Starting with "inte" maybe makes the whole sentence feel a bit stronger.
Talar is in the third position there and not the second. Sounds weird to me anyway, but then again I'm just a learner too.
Null is a programming term that basically means "does not exist". Perhaps the software glitched.
Nope, antingen ... eller.
Han svarar antingen på tyska eller på svenska.
He answers either in German or in Swedish.
Neither ... nor is varken ... eller.
Han talar varken engelska eller finska.
He speaks neither English nor Finnish.