They're both grammatically correct but mean slightly different things; I dont think anyone asked your opinion. = depending on the context sounds like a negative, someone doesn't care what someone thinks. I dont think anyone asked for your opinion. = could be positive or negative, it could be dismissive or it could be inclusive, depends on the context and the tone of voice. But if you're just asking if both sentences work, the answer is yes.

The second one is right ! "ask" is a intransitive verb.when followed with a object,it needs a prep!

I don't(do not) think anyone asked your opinion. I don't(do not) think anyone asked for your opinion.

I dont think anyone asked your opinion.(question) I dont think anyone asked for your opinion.(request)