Umm, don't remember about the 2 spots for 2 clubs, but you only need to be a member of 1.
Now to answers:
1) Whichever you want, it's really up to you. I'm a member of HSCCQ, Rob and Mel are members of BSCC. I believe Teddy and Nick are members of HSCCQ too. Usually it depends on what sort of motorsport you're interested in, as different clubs specialise in different things. HSCCQ concentrate mostly on motorkhanas and khanacrosses, while BSCC concentrate mostly on rallies (both dirt and tarmac). There are other clubs too, that do different things (like IWMAC concentrate on autocrosses, and the MG Car Club concentrate on hillclimbs).
That said, most car clubs run multiclub events where anyone from any clubc can join, sometimes it's more expensive for non-club members.
Also, membership fees vary from club to club, HSCCQ appears to be the cheapest.
Most clubs will be able to accept your money and forward the forms to CAMS, or you can post it to the CAMS office in Milton, or go there personally.
2) No
3) You can either turn up at an event, most clubs will be happy to take your money and forward the forms to CAMS, or you can post it in, or you can turn up at the CAMS office in person. Again, up to you.