Hi AMS-LHR,
Welcome to BA! Your posts remind me of my first joining the airline some years ago, all the questions and excitement! I'm sure you're going to have a ball!
When you nightstop, 99% of the time you will return to base with the same crew as your outbound. However, in a few instances you will be on a different itinery to the outbound crew and join a different crew for the return sector. I do recall some split duties (last flight out, first flight back into LHR) having this arrangement, although I'm longhaul crew now so I stand to be corrected.
Earliest report for Eurofleet is the 5am Paris. A trip that you really want to avoid if you're coming in on public transport. However, when I was on EF I always bidded for late starts and I rarely saw this trip on my roster. You would be surprised how many crew like this one - gets you back by about 11am IIRC! Not bad for a days work.
The Aurora across the road normally charges around £60 per night. It's fair to say that it is increasingly difficult to book a room here, the last couple of times I tried they were fully booked up. In fact even some back to back crews on longhaul often stay in the Aurora Park in Colnebrook as it's often chocka! There are other, less expensive, options all along the Bath Road and most will do a crew discount. Also, keep an eye out in the Compass Centre - there are lots of ads for B&B's, crew rooms etc at good rates and some are run by crew or ex-crew.
The facilities in the Compass Centre are good. There are showers, washrooms and storage areas for your luggage. There's also the infamous canteen, and a coffee shop (singles bar). However, the Compass Centre is winding down it's operations as most departments are being relocated in preparation to the opening of BA's saviour (haha) that is Terminal 5. I'm guessing by the time you come online there will be only six or so months before T5 opens so perhaps there will be less facilities available than there are now.
There are also 'quiet' rooms in the Compass for those who wish to get a few mins/hours shuteye before operating. You are not able to 'camp out' here overnight though - I know from experience! The Compass Centre most definately closes down once the last of the crews have been sent home from standby. If you're caught after that you'll be turfed out. I have known people to sleep in their cars before!
Anymore Q's, give me a shout!