1) No
2) Should be able to, I think - however, make sure they have what they need in their carry-ons.
3) Yes - the fee is 500 Baht per person (about 12.50US), payable only in cash - there are ATMs there which give currency in denominations of 1000B notes.

I don't recommend that they stay at the Amari Airport hotel as it's really quite overpriced for the quality of hotel that it is - although it's the only hotel that actually connects to the airport itself. You can pretty much get to any major hotel in town for under 400 Baht in a cab.

Editted to add - not sure what kind of travelers your parents are, but the NW flights generally arrive around midnight & chances are they'll be awake anyways due to the time zone change - if they have a morning flight out, spending the night at the Airport isn't a horrible option, IMHO. Of course, my parents would never consider doing that - but there's a 24 hour bar/restaurant & Burger King & a 7-11 in the airport & the internet center's (though expensive) is open 24 hours too. If they choose to not go landside & have the ability to enter a lounge, I think the CIP lounge is a 24 hour lounge too (which gives access to Plats AND Golds according to their sign) - the 2-month lounge pass is only 85 bucks, so this may be worthwhile to buy one for them before they go on their trip.