- The spell "Create Undead" says the corpse becomes a ghoul:
You can cast this spell only at night. Choose up to three corpses of Medium or Small humanoids within range. Each corpse becomes a ghoul under your control. (The DM has game statistics for these creatures.)
Cast at higher level spell slots, it does indeed allow you to create mummies and wights.
When you cast this spell using a 7th-level spell slot, you can animate or reassert control over four ghouls.
When you cast this spell using an 8th-level spell slot, you can animate or reassert control over five ghouls or two ghasts or wights.
When you cast this spell using a 9th-level spell slot, you can animate or reassert control over six ghouls, three ghasts or wights, or two mummies.
- The spell tells you the normal way to keep control:
The creature is under your control for 24 hours, after which it stops obeying any command you have given it. To maintain control of the creature for another 24 hours, you must cast this spell on the creature before the current 24-hour period ends. This use of the spell reasserts your control over up to three creatures you have animated with this spell, rather than animating new ones.
But, yes, another way to do it is to use command undead -- but that is better used on enemy undead.
- Yep. Until it gets killed again. Then find more corpses.
Note: Skeletons and Zombies turn into mindless killing machines when not controlled, read the description of them in the monster manual. I think given the Monster Manual description an uncontrolled Ghoul would also not be friendly to the caster, being "driven by an insatiable
hunger for humanoid flesh." Uncontrolled mummies aren't covered, as they generally are created for a task and tend to just keep doing that task given the Monster Manual description. Unbound they may just wonder away.