Are you sure? As far as I know, Slingbox and Vulkano do not require a static IP. In fact, my home cable connection is not a static IP and my Vulkano works just fine.
Yes, very sure, at least with the Slingbox.
Verizon 4G LTE will assign you an IP range that can not routed across the Internet and can only be used on local networks. You will sometimes see these used on ISP networks, where the devices can only be accessed from within the ISP's network, not from the rest of the Internet. This is allowed under RFC 1918, do a Google search for it.
And don't listen to people who say all you have to do is do is utilize the services of a DNS server, IT WON'T WORK. Just go on any forum on a DNS hosting site and ask (about RFC 1918) before you go through the trouble.