Your friend is right, that new motherboard would need DDR3 RAM. It is possible for you to upgrade to an AM2+ (instead of AM3) motherboard that would support the 955 BE processor as well as your DDR2 RAM if you wanted to save some money now, but DDR3 is the way things are going. Up to you!
Yep, you've got a nice motherboard and decent RAM. I prefer fancier memory usually, but that stuff will do the trick.
I'd personally pick either the Gigabyte GA-MA770T-UD3 motherboard or the Gigabyte GA-870A-UD3 if you can get them instead, but thats just my preference. The Gigabyte 790/890 boards are quite nice also if you did want to keep that particular chipset.
Nah nothing really, I just prefer them personally. As for motherboards in general though, Asus ones are perfectly fine - just make sure you're not paying for a bunch of extra stuff (like extra PCI-E video card slots if you're just using 1 card).