You can only access Bthardamz if you've started Peryite's daedric quest, issued to you if you visit his shrine.
You cannot access Bthardamz unless you are on a mission for the daedric lord Peryite. The shrine of Peryite is east of Bthardamz, and a little south. Once you are on the mission, you'll be able to get in, the vines will disappear. If you are indeed on the mission and you still can't get into Bthardamz, then you've got a serious bug and may have to wait for a patch.
On the coast, northeast of Dawnstar.
Any that suits your playstyle.
No.
There's nothing to join, you just buy the game and start playing.
If you mean playing it then yes, if not, then it's up to you.
yes, there is a path from the town at the base of the mountain all the way to the Greybeard's front door.
There are no fixed locations, they just start appearing when you are at a high level.
Skyrim is known for it's crashing, but not EVERY time. If you were being serious about it crashing every single time, possibilities are that your disk is scratched, you have currupted data, or you need to download an update.
You have to complete main quest: dragon rising
You need to be Lv20 to start the 'Pieces of the Past' quest.
I would advise that you start off as a dragon. The dragon has the best perks.