I would like to know if the SB 800 is compatible with the G 10 or do I need yet another flash.
You'll get auto exposure flash only with Canon EX flashes (and possibly with 3rd party flashes engineered for automation with G10). According to the G10 manual, other flashes "may work manually or not fire at all."
So it seems, at best, your SB800 will only work in manual mode with the G10.
The G10's built-in flash, like most of the breed, works only at close range, and I use it mostly for fill-in light.
Oh - one other thing - I don't know Nikon gear, but if the SB800 is a full-sized flash, it will overbalance the G10 and make it severely top-heavy.