"A green pepper is also a vegetable" is correct too.

"Is also a vegetable" should be correct

Yes I agree. I would say "is vegetable too". Or "is also a vegetable".

This appears to be incorrect grammar, at least in English

While literally equivalent, syntactically English still prefers also to be near its verb. I think both should be right.

why is green pepper not accepted in favour of bell pepper. Reported

I agree with all the previous comments.

Sometimes it's only accepted the literal writing