No. The iphone 4 uses a micro sim so the sim from the older iphones won't work. There should be a sim in the new phone for you ready to go though... the old sim will self destruct upon activating the new one
as everyone else said, diff. SIMs. but - you can call 611 from your old phone, and it should prompt you to activate your new device. Follow the prompt and new phone will be activated with new SIM. Very easy and takes 15 seconds.
It is, but what a pain in the butt. If you don't have a microSIM on-hand to use as a guide/template, I've gotta think the chances of getting it right without destroying the SIM being modified are probably pretty slim.