Purchased a new home, owner had tons of things on walls. Lots of anchor holes (some with plastic anchors still in there) and rips in drywall paper (not large but many).

Should I repair with wallboard compound or fast drying spackle?

Should I try and pull the anchors, force them into the wall, or just imbed them enough to compound spackle them?

Can I use a hair dryer to speed drying process when I need multiple coats?

Thanks for the advice!