... A 'blanket' over what? What is this blanket made of?
The insulation under the crawl (assuming it's NOT heated), should be R-30 or more. It should be installed with the Kraft side facing the INSIDE of the house; NOT the ground.
YES, most definitely, the old insulation is to be removed. Wet, compressed insulation is useless, or drops the R-value dramatically! Insulation, in order to do it's 'job', needs to be dry and NOT compressed.
The new insulation should be 'hung' which allows it to trap warm air. If he's STUFFING it up there and putting up these metal 'hangers/wires', the insulation is losing its value. I did my crawl a few years ago and used nails and string to create a 'spider web' under my floor joists to keep the insulation from falling down/out. It's OK for the insulation to 'fall' on itself as long as nothing is actively 'compressing' it downwards. Consider doing this or using chicken wire to hold it up.