I would, but it won't last long.

Yes, you can use that for mulch or just turn it all back into the pile and finish it off as compost.

You could use it for mulch, if there is enough, or you could put it back into the composter to be worked on some more.

Yes, rough compost is an excellent mulch---almost none better! I like a mulch that breaks down quickly, because I depend on my mulches to feed my plants.

Mulch is more benefitial in some areas than others. If you live in an area with very hot sun and little rain it can be very good solution. If you on the other hand live in an area with regular rainfall, not so hot sun and it is not a problem to keep the soil moist and plants watered enough, then the finished compost is a better additive to the soil.