Would Voldemort need to kill him personally for this to work? Why?
Yes. Voldemort isn't Harry's Universal Horcrux.
Having taken Harry’s blood into himself, Voldemort is keeping alive Lily’s protective power over Harry. So Voldemort himself acts almost like a Horcrux for Harry (JKR FAQs, "What exactly happened when Voldemort used the Avada Kedavra curse on Harry in the forest?")
Harry's blood in his veins ensures that Lily's protection works - and Lily's protection is very specifically against Voldemort trying to kill Harry.
If Harry could come back after the attempted killing, could he have come back indefinitely?
It's not known from canon. I don't see any clear indication that he wouldn't.
The closest thing we have to an answer is JKR's clear insistence that Harry's sacrifice and Elder Wand both played a role in how things turned out (from the same FAQ linked above); AND that this isn't like a repeatable scientific formula:
Voldemort is also using the Elder Wand - the wand that is really Harry’s. It does not work properly against its true owner; no curse Voldemort casts on Harry functions properly; neither the Cruciatus curse nor the Killing Curse....
It is important to state that I always saw these kinds of magic (the very deepest life and death issues) as essentially un-scientific; in other words, there is no “Elder Wand + Lily’s Blood = Assured Survival” formula. What count, ultimately, are Harry and Voldemort’s own choices. They have each been given certain weapons and safeguards, but the power of these objects and past happenings lie in how they are understood, and how they are used or enacted upon. Harry has a deeper and truer understanding of the meaning of the objects and past events, but his greatest powers, those that save him, are free will, courage and moral certainty.
Basically, if given 100% identical situation, the outcome might be the same. But if some variables change (Harry isn't choosing to sacrifice himself; OR Voldemort doesn't use Elder Wand, OR Harry looses ownership of Elder Wand, or....), then the outcome might well be Harry's death.
