1)It will be a massive improvement, but I'd get the 7870 instead. If you don't want to OC you can get a -3450 or -3470 and a 7950, which is even better.
2)It should be OK, but I'd replace it fairly soon.
3)You could upgrade the GPU now then the platform + PSU later, and get something you can CF/SLI on if you want. Or you could use the E8200 and a cheap GPU for an HTPC or something - they're still pretty capable. The GTX260 is a bit hot + noisy for anything much now.