Is it possible to use same modem firmware on different phones?
No, you can't flash firmware designed to work with one android device to another one.

There are some bizzare situations where this does work because devices have identical hardware (Coolpad F1 and Micromax A310), but this is very unlikely to happen and you shouldn't try it.

As for a device backup, you can make a nandroid backup using CWM or TWRP and copy it to your computer.