yes. and no. 😊 an american would completely understand and/or use both BUT the first sentence is TECHNICALLY not correct. correct grammar would be: “i answered all the questions correctly.” but no american would say that- it’s too formal. we would use either depending on which part of the country you’re from. if you just want to be understood and don’t care about being formal, both are fine. if you want to be CORRECT, use the second sentence. 😉

No, those are not the same meaning. One is about the question and another one is about the answer.

I think they more or less mean the same thing. But like mike said, first one is technically wrong, even though native speakers can and do say that sometimes. It usually happens when I'm speaking quickly. But if you are being scored for making or asking questions, I would say that it would be correct to say "I got all the questions right".