Is the Army still keeping Guardsmen (who are injured on deployment) on active duty orders upon demob while they are treated and recovering?

Unless they changed things, that is what the WTU is for, most active bases have a WTU for wounded active, guard and reserve soldiers. Guard and Reserve soldiers will remain on active pay until they are deemed well enough for discharge back to their parent unit. The WTU was originally staff by 50% active component, 30% Guard component and 20% Reserve component to help support those wounded soldiers.

Yes. They go to the WTU at the demob site, if there is a military base close to their HOR they will be transferred there. When I got home in 16 a fellow soldier who was injured went to WTU at ft hood and a month or so later was transferred to the WTU at ft Bragg.

Yes they are but it also depends on the nature of the injury/illness. There are programs where they transfer you to a type of home station care. Some are kept on orders and some are not. Again, depending on the treatment plan.