Our Airline I have found to actually be fairly reliable in terms of sticking to the published schedule (although it does change relatively often) - the link to Brisbane is vital for the country, so it is pretty important that at least that portion of the journey sticks to schedule. There is often a fuel stop in HIR, depending on freight uplift, and sometimes whether there is enough fuel on Nauru.

They are a nice airline - old planes, but very personable and friendly crew.

Getting accommodation on Nauru however is extremely tough - the Regional Processing Centre and associated staff take up pretty much all accomodation on island, so I would make sure you have somewhere to stay before you book your flights. I would recommend the Ewa Lodge if you can get it, rather than the Menen Hotel, which is the hotel most commonly cited for visitors. The Ewa Lodge is attached to Capelle & Partner, which is basically the only real shop on the island - http://www.capellepartner.com/. You can hire a car from them as well, which you will definitely need.

Let me know if you have any other questions about Nauru - there is really no place like it!