Hey Nick, answers as follows;
1) Using tmsh: show ltm profile http-compression 'name'
2) No, this will result in compression occurring twice if the servers also support it, once at the server then again at the F5.
3) It's not definitive but you can view some statistics in the GUI here: Statistics menu path: Statistics > Module Statistics > Local Traffic > Profiles Summary > HTTP Compression. The tmsh command I mentioned in 1) also shows this.
4) As long as you are terminating SSL/TLS on the F5, it'll work just the same. If you are not, you can't compress the traffic.