Do you have to give a thirty day notice on the first of the month?
Or can you give it in the middle of the month?. and have your rent prorated?

You give notice the same way you rent the premises - if you are from the 1st to the end of the month, then you give notice prior to the first.

No, you are not entitled to prorated rent in any State I know of - unless, of course, the landlord immediately rents out the premises and is not "out" any money. He cannot collect rent from two people for the same time frame.

The 30 day notice should be to the end of a rental period. Watch for 28 day months.

Unless your lease allows for a pro rated rent then no most landlords will expect full rent for any partial usage of the rental