Should the wiring to my recessed light have a strain relief and a ground wire connected?
There's several problems here:


The ground wires seem to be missing. That looks like yellow Romex (12/2, with ground). You need to ground your light fixtures and the box (which is why the box has that ground wire)
They ran 2 wires into the same hole (normally you put one per hole)
The wires are simply electrically taped together
The rail should be attached to joists on both sides.


What they should have done was use a NM wire clamp to hold each wire in its own hole.



The clamp holds the wires firmly in place, and prevents the wires from rubbing against the metal box (which could cause a short, and potentially a fire)