Can it be used in combat? Do all sorts of summons, applied outside of combat, have no time limit? How long does the raised undead exist? Can you order a summoned character to commit suicide?
It exists until it is killed or the necromancer orders it to die.
You can order it to do anything.
Is unattractiveness determined by mutation or a GM roll? Can mutations result in supernatural abilities?
Like telepathy? Yes, they can.
Does "initial health" refer to the target's health at the moment the spell is used?
Can a dead friend be a monster/animal? Due to the lack of will, can it (and other undead raised by a necromancer) only replenish health through the necromancer's magic?
Only.
Is it determined by the player or the GM?