Air Berlin - Have you flown this airline?
 

Wondering about Air Berlin.

Has anyone flown them out of JFK to Europe? What are the planes like? Entertainment, food? Personnel?

It is the second largest German airline, in business (under the former brand LTU) for 40 years.

New planes, reliable, good. Highly recommended.

Do you know if you can reserve seats in advance?

Look it up on their website. Select Services then Online check-in and it says

Web Check-in
[...] Once you have entered your booking reference number and your surname you can select a seat and print out the boarding passes for yourself and up to nine persons travelling with you.[...]

So you can't reserve a seat when you buy the tickets, e.g., before you check in?

You might find some useful information on this site about AirBerlin seat maps

http://www.seatplans.com/airlines/Air-Berlin