I don't trust a 300W stock PSU on a 8800GT card. But hey that's just my opinion, and opinions are just my thought's on it.
As far as the other PSU upgrades, I would just caution to make sure it will 1)fit the stock psu area and 2) have the same pin outs on the mobo connectors. I have tried to replace the stock psu on a few brand name pc's in the past only to find that their mobo pinouts are a little different. They may not be in this case, just a word to the wise, CHECK. If they are the same, hey go for it. That Antec Earthmuffin PSU should be ok or the thermaltake.
Comming from a Dell 521 owner w/305w psu (backup system)
Yes it can, but for how long?
7800GT you would be ok with (20w less than 8800GT)
You can with the sata to molex adapter.
But for piece of mind why not spend $35 for a 30amp/80% efficient psu with the dedicated pcie x16?