My experience one month into FF14 , some questions.

[KageTokage]

Healers are rather heavily encouraged to deal damage when no one is in immediate danger of dying...though you lose considerably more group/raid DPS whenever somebody dies from a healer slacking, so keeping everyone's HP at a safe level should always be their top priority. The best healers know precisely when the heavy spikes of damage happen on a fight to fight basis and output just enough healing to keep everyone alive, which is better both for their MP pool and their DPS.

And as previously stated, any random joe can become a mentor as long as they meet a few arbitrary requirements on either DoW/M jobs or DoH/L jobs and the vast majority don't actually care about helping people. The Novice Network culture also varies considerably between servers, and I don't think Gilgamesh is known for being one of the more hospitable ones.