can only use right hand to brake reliably, due to disability - safer/possible to modify bike?
Generally speaking your off hand should be the front brake, so if you're right handed the front brake should be the left. They can be set up either way, though, especially if you're using cable-driven (non-hydraulic) brakes. Even with hydraulics you should have no problem making the right hand brake the rear. I would highly advise this, as in a panic situation while mountain biking if you grab the front brake hard, you're more than likely going over the bars. 

There are levers that work both brakes. They are out there!



Here is one that pulls 2 cables at the same time, so you could use it to pull both the back and the front brakes.
http://www.jbi.bike/web/checking_product_description.php?part_number=13748

There is also a company called Surestop whose product I believe works off of one lever and won't engage the front brake until the rear is already engaged, thus making it very difficult to catapult yourself over the bars. They are for V brakes only though, I believe.

The backpedalling braking is indeed a coaster brake: you are correct on that note.