Oceania (Australia, New Zealand & the South Pacific) - ETA (E Visa)

Ok, so I'm going to Australia in December. Well... once I renew my passport and then book the ticket.
Here are a few questions.
1. My ETA was done by United Airlines and they put it as business. I am unsure if they had corrected it (I was there on holiday. I flew on business class so it was UA's mistake) I'm going in December, is this really going to do anything?
2. My passport is up for renewal as it expires in May. Australian entry requires my passport to be 6 months before it expires. Would this invalidate my visa?
3. Is my ETA even still valid?

Key Facts:
-Went to Australia in August for 20 days
-US Citizen

With a new passport you will need a new ETA, as they are tied to the passport number. There may be a way to transfer it, but it's probably much easier to just get a new one.

The ETA visa automatically ceases 12 months after grant or upon the end of the life of the passport. There is no way to transfer it to a new passport.