Tor circuits change every 10 minutes. If I leave the Tor browser open on my computer, or the Orbot app connected on my Android, will I add any network overhead for the network? Should I disconnect when I'm not using Tor, or will the client automatically stop creating new circuits until I start using it again?
For the Tor network, it is fine to leave your Tor Browser open when you're not using it. Tor will occasionally build a few circuits, but only relatively few, and after a bit it will stop doing even that until it receives a request from your browser.
The only thing it will keep fetching every few hours is new information about the available relays. So if a couple of megabytes extra are an issue for you because your internet connection is slow or you have a data cap for mobile, you should turn it off if you won't use it for a few hours.
No, you should not - you can't add any "overhead" by staying online. A hint : make it a non-exit relay, forward a port and make two lines appear in your torrc :
ClientOnly 0 ORPort 443
It will improve your Tor experience greatly, by the way - it will be a way faster. I just picked port 443, you can pick another one. If you need help doing that - just say it, I'd like to help!