1) You can use a booster.
2) Only the level of magic on the caster at the time of casting the global matters, so yes, you can take the booster off after you've cast the spell. A mage only counts as dead if it is neither alive nor undead.
Yes, he's just clarifying that Undead will qualify as "living" per the stipulations of having a global, though they are not technically "alive" - so just stating that they must be "alive" would be just as confusing as saying "alive or Undead".
Don't make them dead or re-dead, and you'll be fine.