Since you are an Avatar fan, the Astral is not like the spirit realm in the show. Assuming you also watch Korra, Astral Projection is basically what Jinora can do in the later seasons. Traveling around the physical would be considered Ethral Projection I believe, but how she got to the spirit realm in the book of spirit is basically Astral Projection.
I've never tried 'bending' in the Astral, but I think you can. Some people don't believe in the Astral because of how open it is in terms of what exists there and what's possible. Try and discover for yourself.