Some backup and restore questions?
Backups only contain your data, not the firmware. If you restore a device that's been upgraded to a new OS version from an older backup, you keep the new OS version. (This is, in part, because this is how iOS upgrades used to work: backup, wipe-and-install, then restore.)

It's actually pretty difficult (but not entirely impossible) to talk an iOS device into downgrading to an older version of iOS.

To your second question, I'm not certain of the degree to which you can cherry-pick what to restore from a backup. I've never attempted to do so, as I'm usually interested in restoring the entire previous device state. I imagine that it would be straightforward (if time-consuming) to simply restore everything to the device then remove what you don't want.