Yes. Your motherboard should have a PIC-E 16x slot.
As far as power requirements. AMD recommends a 500W PSU. That is total system requirements. Honestly, if you have a 400 or 450W PSU that is of high quality with maybe 30A available on the 12v rails, you would be ok as long as the rest of your system isn't drawing tons of power. If you are into Overclocking and alot of high end components I'd stick with 500W.
AFAIK card with PCI-E 2.1 standards such as 6850 often have problem with PCI-E 1.x. normally the problem solved through BIOS update but if the mobo maker did not release one then he will have to use mobo with PCI-E 2.0.
Yeah, I still not sure whether 2.1 cards will works 100% on 1.x slot or not.
Better play the safest way, get 2.0 cards or borrow HD6850 from your friend and try on your PC, if that works then you can continue your plan to buy 6850.