1. Are we assigned a PVP and if so, when do they make contact?
no. You can request one through the website. I think they can 'take over' your booking.
2. How do upgrades work? Do you just get a random offering?
upsells are not offered on every cruise, and they are completely random. My advice for you would be to bypass the offers for your trip since your booking with 8 kids will most definitely complicate that. you are unlikely to get offers for enough cabins in the same area.
3. How about price drops? Does Carnival honor them and if so, do you just notify your PVP?
if you booked early saver, you have to track price and submit to Carnival. I believe a PVP can do it as well.