Danger said:
Can someone explain in simple terms exactly what goes on?
A high fraction of the time, your computer's processor is idle. Hit ctl+alt+del and hit the performance tab and watch the graph. Typing this sentence, the usage on mine never went above 5%. Seti@home (the original distributed computing project) and Folding@home use that 95% that you aren't using.
Is it a guaranteed safe site (I got fooled by the BBC fake)?
Yes.
Does it affect what I can do with my computer while it's running? (Like, will it interfere with my own programmes or PF sniping?)
No. Newer operating systems are capable of multitasking, load balancing, etc. Essentially, the SETI or Folding thread is assigned the lowest possible priority, so it will always get out of the way of whatever else you are doing. Out of curiosity, I've tested my computer - playing games, running benchmarks - and there is no difference in performance of the system.
The one thing you do lose is the memory. I'm not sure about folding, but SETI uses 16 megs. On my system, I currently have about 200MB free, so its not something I notice. Unless you're short on ram, you won't either.
What happens when I go off-line or have to reboot? I'd like to participate if the answers are agreeable to me. Thanks.
The program is capable of being completely autonomous. It picks up where it left off when you reboot and downloads new data to analyze (and uploads the old data) automatically if you are always connected, or it warns you that it needs new data if you aren't always connected.