Bookable on Airberlin.com
most dates available. (except those grabbed by people already )
Keep in mind you probably won't be protected by EU compensation and doubtfully will be reprotected if there are issues with your flight.
Travel insurance won't cover because they already announced bankruptcy?
Idk about travel insurance , airline bankruptcy might not be a coveted event but I imagine you'd be covered for the price of the ticket at least, maybe not to rebook you. I'd hope the later
I saw RT from TLV-JFK for $440 or OW for $240 on www.studentuniverse.com. Flights up until November shouldn't be an issue.