Question about upgrading cpu (2500 to 3770)

So I just bought a 3770 as a cheap upgrade. I had two questions actually;

First, does anyone know if the stock cooler from a 2500 will work with the 3770?

Second, according to pcpartpicker, my mobo brings up a compatibility issue saying that I might need a different chip to upgrade the bios before putting in the 3770. Obviously, I have a different chip. How do I know if I need to update the bios? Can I go ahead and do it while I'm waiting on the new chip to arrive?

Thanks!