Yes, they will work. Link speed will be halved, but apparently it has very little effect on performance.
Yes they will work just fine. It could be beneficial to update your BIOS to the latest rev before hand, however.
Just stay away from 2.1 cards, they are sometimes iffy in 1.0 slots, but 2.0 are fine.
Yes, I actually have a brother in law running a Sapphire rev. 2.1 HD5770 in his crappy nforce 630i motherboard with a rev. 1.0 pci slot and it works fine. It works on his but that doesn't mean you couldn't have problems with another board or card.