I am currently using ArduinoDroid and a cheap android tablet to program my arduinos on the go (see last sentence for details of that).
What exactly do you mean by "program my arduinos on the go"? Are you just using it to upload sketches to your Arduino boards, or are you actually doing significant development writing code on the tablet?
(1) who is using git (locally) or GitHub (online) for Arduino development?
(2) I have access to Termux (so can install git on the Android device) and think having a local git repository, synced with GutHub would be good for version control - any drawbacks?
In general, this is very good and there are no drawbacks other than having to spend some time learning to use git and GitHub. As for the Android-specific aspects, I have no experience.
(3) long-shot but is anyone using such a setup (android Arduino IDE + Git?) It seems to me the setup could be quite a challenge
I have the same feeling about it being a challenge. I think doing serious development work on a cheap tablet could be very challenging in multiple ways.
Perhaps with a real keyboard and mouse attached, it would be acceptable, but if you're going to do that it might make more sense to just get a cheap laptop instead. Trying to do real work on a device without a proper keyboard and mouse, no thank you.
Next you have this ArduinoDroid thing. I don't know how well that program is maintained but it will always have to follow behind the lead of the Arduino IDE. I suspect you'll always be running into limitations of ArduinoDroid like standard features of the Arduino IDE that are not implemented, toolchains that haven't been ported to work with Android, etc.
Then you have the possible difficulties of running git on Android, which I have no knowledge of. I like using a git client software to provide me with a GUI. I'm perfectly capable of using git from the command line but I find a well designed GUI makes common git tasks faster and easier. You will likely be very limited in your options for a git client, and my experience is that even with the much larger range of options available to a Windows user, most of them were still horrible. I was very lucky to find a good one after much searching.