New CPU

1) Yes, possibly with a bios update. Here is a link to possible cpu upgrades:
http://us.msi.com/index.php?func=prodcpusupport&maincat...

2) No extra cooling is necessary.

3) I would expect to see no massive game improvements. Gaming is usually limited by the graphics card. A 9400 GT is not that strong of a card. Conduct these two tests to get some insight on what to expect:

a) Run your games, but reduce the resolution and eye candy to a minimum. This will simulate what will happen if you upgrade to a stronger graphics card. If your FPS improves, it indicates that your cpu is capable of driving a stronger graphics card to higher levels of FPS.

b) Keeping your graphics resolution and settings the same, reduce your cpu power. Do this by removing the overclock, or by using windows power management to set a maximum cpu% of perhaps 70%. If your FPS drops significantly, it indicates that your current cpu is a limiting factor, and that a faster cpu would help.

4) No i3/5/7 processors are compatible with your motherboard.

5) I suggest you consider upgrading your graphics card first. Jump to something like a GTS250 or better.

6) A mild overclock is possible, but don't expect much.

If you still think you need more CPU power, look on ebay for a higher clocked duo like the E8400. They go for $120 there.
I suspect though, that that $120 would be better spent on a graphics card upgrade.