My phone has died, the screen went black and it won't stay charged, do I have to come up with money for a new phone or would it just get added to the monthly payment ?

As long as your account is current they won't charge you they can add it to your bill, but if you have a past due balance you'll have to pay that first

I find it better to call Verizon's Tech. Dept. They are totally helpful and go the extra mile to fix any problem. The main function of Verizon stores, which are mostly franchises - is to sell, not to repair. That is a direct quote to me from a number of them I have run into over the years if I found I was passing one and had some minor problem. So I would just call Tech.

Take it to your closet verizon store they can help you