Cause of misfire in my engine

A week after I purchased my 2006 GMC Envoy Denali, we finally did highway driving. Half way to Cindy had issues that we found was cylinder six misfire. Car lot fixed problem. Got it back and timing was off, gave it back, they said they turned and timed it. Clearly it was fixed, but no proof of tuneup, no nee plugs or wires.

About three months ago I noticed a slight lag. I procrastinated. Took it back to car lot and now cylinder seven misfiring and pretty much dead, or 100% dead. They told me to drive it because it would not break down anytime soon. They told me they could get a warranty on my truck at any time and that a $215.00 deductible, paid by me, would cover new engine and transmission. They told me to wait until after the first so it is financially easier on me, rather than right before Christmas. So that leads me to believe the cylinder was not totally dead. But they did not unhook fuel injector from that cylinder. They did not warn me of the fire hazards with the catalytic converter. So what caused it?

Right now, we think the head gasket is gone or almost gone, white smoke sometimes bellows out exhaust, but also, sometimes does not smoke at all. Happens at different times too. Sometimes when I start vehicle, sometimes when I accelerate hard, and sometimes when I am idling on a hill. We smell burnt oil and we have to fill coolant every few days. Noticeable decline of power since the smoke started. It also has a shake/stutter when idling.

What is causing these misfires?
1) Loss of spark (worn, fouled or damaged plug wires, or cracked distributor)?
2) Air fuel mixture out of balance (not timed)?
3) Loss of compression?

So if they tuned it up after the first cylinder issue, could root cause be plugs and plug wires?
Did they just time it and not do a tuneup?
Or did they not even time it? And that would cause the air fuel mixture to be unbalanced.