Current AMD X2 build - Few Questions on Upgrades

Hi all, I have a few questions on my computer. To give you a little about myself and how I use the computer, here is a short description. I mainly use the computer for web browsing and gaming (Team Fortress 2 and Call of Duty 4). I might be looking into gaming with some newer games, mostly FPS games. At any given time, I might have one Firefox window open with about 5-8 tabs, iTunes playing music, Pidgin, multiple MS window managers, perhaps 1-2 PDF files, perhaps 1-2 Word/Excel/etc files, and that's it... I think 3dmark rated my CPU at ~8700 if I remember correctly.

AMD Athlon 64 X2 5200+ Windsor 2.6GHz
SAPPHIRE Radeon HD 3850 512MB 256-bit
MSI K9A2 CF-F AM2+/AM2 AMD
G.SKILL 2GB (2 x 1GB) 240-Pin DDR2 and G.SKILL 4GB (2 x 2GB) 240-Pin DDR2 SDRAM DDR2 800 (PC2 6400)
Sony NEC Optiarc 20X DVD±R DVD Burner Black IDE Model
Cooler Master CM 690 Case
Seagate 500GB HD
Ultra V-Series 500W PSU (+12V, 28A)
Windows Vista 64 bit SP1

1) Is it worth to upgrade to a quad core? The performance of my current system is ok and good enough for me, but I haven't tested a X4 system and don't know what to expect or know how much of an improvement would come... Also must I get the BE if I want to OC a little? (not too mucH)

2) Will my motherboard support the new Phenom IIs? I see only "Phenom" listed on the Newegg specifications page... http://www.newegg.com/Product/Prod [...] 6813130138

3) Is my motherboard acceptable - in other words, is there any reason to upgrade it?

4) Is it a smart investment to upgrade to a better PSU and wipe out the Ultra I have right now? (I got the Ultra free AR so I used that for the time being). What do you think about http://www.zipzoomfly.com/jsp/Prod [...] y_10009333 or

5) If I get the Phenom II X4, is it required that I get a cooler/HSF? If so, can someone recommend a good one?

6) Ok - this isn't a real upgrade question, but perhaps might lead you to suggest something to upgrade that's causing this problem. Sometimes, my computer just shuts off and restarts randomly. This can either happen when I'm in game playing TF2 (mostly this) or when I'm browsing Firefox with a few tabs open. Does anyone know what the issue is? Perhaps which compoment may be the culprit? Also is there a way to check the latest errors in a log or something in Vista?

Thanks all! Sorry for the long post and many questions!!