You won't have any issues driving across the border; I've done it many times in Hertz cars. No special paperwork, insurance or otherwise is required.

You can't use your double upgrade voucher to get into any prestige cars. If you want a prestige, you'll have to book a prestige.

The voucher should have a PC code for the upgrade; so when you make your reservation you would use the BMI CDP code and the PC code for the voucher, which would let you get upgraded... at least in theory. My experience with upgrade vouchers is that they're only sometimes honoured.

Finally, note that the manhattan locations sometimes have very high rates so depending on your flexibility you might consider pricing a pickpu in Stanford, CT or Newark airport and taking the train to get the car.