Two out of three......
Home phone use, NOT internet (unless you had a dial up account with some ISP). And yes, you can take the small box with you anywhere you get Verizon service, but you have to have a phone to plug into the box. It's not 'cell phone' as such, though the box does use cell service from Verizon to your home phone. Instead of plugging your home phone into a phone company wall jack, you simply plug it into the box. We use a 'base unit' into the Box, with multiple cordless units that connect to the base unit (a completely separate phone unit)
The Verizon box normally plugs into a 120v outlet with a 'wall wart', but it has a small internal battery that allows you to still use your phone (if your phone doesn't need power, most do now) if the power is out, or take it on the road with you. I'm thinking it was good for 8hrs if I recall right.
Verizon also makes a wireless home internet box, but while the home phone box WOULD work for us here ( I suspect it is a higher watt unit and even then we usually get one or two 'bars' out of a potential three), the internet unit would NOT work here....we tried it, and returned it, they have a 15 day trial free here. PLUS you have pretty serious data limits, just like any cell phone plan.
The Verizon box works for us....cut our costs in half, and better service. The POTS system (Plain Old Telephone Service) copper lines are shot in our area...lot of static, down time, etc....which is WHY we can only get 512k internet over the DSL part of it.
Century Link has seen the handwriting on the wall, and will not spend a dime to upgrade their lines/equipment.....they know the whole world is going wireless.