+1 on the 1am-ish airport opening. Palauan hotel operators are really good about letting you know when to head to the airport, as they're accustomed to the early morning flight schedules.
There is a single private lounge shared by all airlines, including DL. It's actually located outside and to the right of the main terminal, and is a space with more character than, say, Delta's lounge at NRT (dark wood, leather seating, good AC, limited food and drink selection, but sufficient). Eligible fliers are given a lounge voucher at check-in. Boarding announcements are clear and timely in the lounge.
Enjoy Palau -- it's a beautiful part of the world, with abundantly friendly people.