There are 2 versions. One is for the old Vive headset, the other is for Pro, Cosmos and Elite. The latter costs a bit more.
So yes.

Yes, as far as I know, there is only one wireless adapter from the first HTC Vive and you can use it all the way up to the Cosmos Elite. You just need a new mounting kit with a powerbank with a little more output power. So far, however, it has only worked for me with graphically less demanding applications. With Halflife Alyx there are always annoying jerks.