While you’re down at Home Depot, pick up an illegal who does yard work on the cheap. /s
I wouldn’t bag it. Let it sit there and decay for a natural fertilizer.
As to the scalping, water it well and let it grow. Also, raise the blade for next time.
Per #2 above - even if your doesn’t mulch, just drive your toy in the direction of where the clipping exit (the side shooty-thing is the technical term). That way you’re mowing over them twice which makes it into mulch anyway - once with the initial pass and second cutting them when you go over them again in tandum with the next row’s initial pass.