Will my p4 dual core processors run win 7 64 bit os?

The 64-bit version will not run well on that hardware. It's too outdated.

yes but will use slightly more ram due to the bigger addressing used. it will free up the extra ram you have so you can fully utilize it but at the cost of using about 1.2gigs of it on the pro or ultimate. basic versions use between 900mb and 1.2gig.
it should run a little better than it currently does. speed wise but yer cpu is pretty dated so dont expect a miracle.

You have a single core Pentium 4 with Hyperthreading tech so...personaly i would try it, it willl fix your "4GB RAM 3,25 usable" issue

Your Pentium 4 is single-core. A Pentium D is dual-core.