1. with 16A on the +12V rail (192W), you'd be pushing it with that PSU, but if you're not running much else from it, it should work fine.
If it were me, I'd get a new PSU anyway. Something like this
with 60A on the +12V rail, high quality components, and ~83-85% efficient across a very wide range of load conditions
2. the 4870 uses the same PCB as the 4850, and is about 8 7/8"
If in doubt, there's always the option of getting a longer IDE cable
3. I've got Diamond's XOC BIOS here
(990MHZ ceiling in CCC; third party programs are unrestricted)
the stock core speed with that BIOS is 800MHZ though
I've made a modified BIOS based on Diamond's XOC BIOS here
, which has a stock core speed of 750MHZ in 3D and 160MHZ in 2D
(normally 500MHZ in 2D) for better power saving, but still has the overdrive limit in CCC at 990MHZ (again third party programs are unrestricted)