Sure, if you're coming in for a landing, you will dial your autopilot down as you are granted clearance. Ultimately you will switch to approach mode which ignores the set altitude and instead follows the radio signals down to the ground.

Yes. Most approaches start from 2000-4000ft.

Extremely common to use altitude pre-select for intermediate level off points on approach. At my home field, the highest such figure is 2000’ MSL and the lowest 720' MSL for an airport around 150' MSL.