Yes, they are both fine. The first seems more informal, so better for conversation. The second is a bit more formal so better for writing.

Yes, both sentences are correct and natural. The first one sounds more casual and is what people would normally say in everyday conversation. The second one is a bit more formal and careful, but still correct. So you can use either, depending on whether you want a casual or slightly more formal tone.

They mean the same, and are indeed correct.