I have a few questions regarding Project. Do we need to run My Sequel in the background?

you mean MySQL? http://www.google.com/search?hl=en&q=Mysql...G=Google+Search

its pretty much a database application especially used for web forums and stuff like that.

since i don't know completly what Microsoft Project Server is, i can't really say if you need it or not... it is needed from what i briefly read from google.