DMV Questions

So I'm FINALLY getting rid of my plates today for my old car (we bought a new one after the wedding). Now the car is registered in my old name but I want to hand in my plates. Does anyone know if I have to change the name on the registration before I can give in the plates?

Also, I'm giving my parents the car so that they can donate the car and get the tax deduction. Do I have to sign over the title to my dad and then he has to register it or can I just sign the title over and he can donate it without registering it?

Any information would help ladies and I feel like 'when in doubt, ask LIW girls'!

TIA!