Is there some way of passing on settings and apps from one device to another on a regular basis?
There is no way I know of to pass on settings to one device or another unless 1) They are the same model of phone and 2) Both phones are rooted. You can back up your current system settings using ClockworkMod backup if rooted, then flash that onto the other phone through ClockworkMod as well. This will share all your apps you had at the time of the backup.
As far as sharing apps, your google account will transfer your apps from phone to phone. Just sign in with your google account and re-install from the app store. You don't need root access to do this.
For either option, to use most paid apps you need to be signed in to your google account when you use them, otherwise they won't work.