UHF set or something else for Mobile Phone

Not UHF, probably HF.

I think it could work on any 2 way radio but it has to have a network and a base with other radios that can recognise the selcall burst.
Its an updated version of the old radio telephone set up.

VKS737 HF tel is charged at $13 a month inc 10 mins of freecalls or $1.30 a min
You can send faxes as welll
Top of the range HF transceivers are around $4k but you can pick up older used units with selcall for a few hundred but you cant add new channels.

I think others can still listen in on your calls

There are 2 ways to achieve suck a feat.
1. HF radio with an interconnect on the base end ie. Radtel
2. Satellite phone.
Both have their advantages and disadvantages, but in the end neither is cheap. Search the archives for more information.