Do half elves cycle through lives like elves do or do they only live once? Is this debatable?
I'm not familiar with this concept (or my memory is really, really bad!). Regardless, Half-Elves normally only have one life. I think 'fullblooded' Elves do so, too. The only race that I know of that has multiple lives is the Samsaran race.
Elves do not generally get reincarnated, although some do. Brightness seekers is a mostly-abandoned concept in the setting.