1) I like the security of being checked in. OLCI has saved my bacon at the 2-hour window before. It is also a habit from my United travel where check-in time is the tie-breaker for certain upgrades.
2) Yes. I am flying USA to New Zealand, (seperate) side-trip to OZ and back, then back to the USA.
3) SFO-AKL (AKL-PER, PER-AKL) AKL-SFO