I am flying to Tampa to drive my sister back to New Jersey because she can not fly due to health reasons. Plus her husband is in N.J. recovering from a Heart attack. Can I rent in Tampa & drop off in N.J.

National was very good when I rented locally but I'm not sure if they'll charge extra to drive/drop it out of state. I always shop around & ask their policies. Check thru Expedia, Priceline, etc too.

Yes

Shop around. I have found different agencies have different policies. You may get a no-charge drop off from one of them (although Tampa to Philly is a long way!)

Yes, you can book a one way rental on their website.

I usually have no trouble with one way rentals. They will just charge you more. You can go online and put in the two different locations and it will give you the price