Welcome to the Forums kaotikvizion!
For starters, never go with TigerDirect for computer parts. They're way overpriced and their service is subpar. Since you're in the US, is suggest Newegg
for everything. Great prices and service.
Q1. Simple answer: No. The board you have is too old for the E6500. Your board only supports the 2, 4 and early 6 series (the one you're looking at is the later 6 series). Also, if you change your CPU, you need to repair Windows using your Windows disk.
Q2. The GTS 250 is a great card for gaming but with that processor it will be bottlenecked, basically meaning it won't run at its full potential.
Q3. Nothing else except for speed. Your board can't handle anything over 1066MHz which is pretty standard.
So... With all that said and done here's what I suggest. Spend some money on a new motherboard. That board is killing your potential setup.
Here is a good simple build:
Motherboard, Processor and Video Card: Newegg.com - Computer Parts, PC Components, Laptop Computers, Digital Cameras and more!
RAM: Newegg.com - G.SKILL 4GB (2 x 2GB) 240-Pin DDR2 SDRAM DDR2 800 (PC2 6400) Dual Channel Kit Desktop Memory Model F2-6400CL5D-4GBNT - Desktop Memory
That'll take about $340 out of your pocket and it's a strong build that will last a good long time. Of course there are cheaper builds out there!
Hope the helps