Good catch on the Eternal Servant. Abilities tend to change names a lot during development, and clearly I was thinkn' of a previous name.
And yes, I would say your conclusions are correct.
I find it very curious that the ability is called "eternal" servant when the Mage's specialty is death, not life. Necromancers aren't about making things last forever, they want to end things instead and keep them ended, and use those ends to gain power. Death magic is basically a way to control a dead body like a puppet. An eternal servant is not eternal because it is discarded when it's controller has no more use for it.
Now that I think about it, it's very interesting that a Necromancer's abilities make him immune to disease and poison and make it possible for him to keep reviving one of his creatures over and over. Those abilities sound more like stalling, avoiding or subverting death, rather than just making it easier to kill things. The piercing for his eternal servant and the ability to do poison damage to anything that's already poisoned makes sense though.
If you were to call it undying servant, then it would at least fit his flavor better because he specializes in "undead" creatures.
Also, the word "undead" is kind of an oxymoron. Un- is a prefix that means opposite or reverse. The opposite or reverse of dead is alive. "Undead" aren't alive, they're dead things being controlled like puppets. They are still dead. They're not in some other state between life and death, it's impossible to be "between" by definition unless you're in a coma or something. "Undead" creatures are still dead and under someone's or something's control or acting automatically for some reason.
Undeath isn't just impossible, it's a contradiction. Either something is alive or not. If part of it is dead and part of it is alive, that just means that it's either damaged or in a coma.
