NET10 uses multiple networks, depending on what phone you have. One can not make any general statement on the phone. I would assume you can't use it.
If you are planning on getting a new phone from Verizon and port your number to Verizon, you can keep you number that way.
Yes, when switching to Verizon I strongly suggest buying or using a Verizon phone just to get the full use of the phone and service.