Hi,
I think Tegel/Berlin is a rather small and quiet airport in my opinion.
As far as I have seen on their website there is no restaurant open during the night (latest 10pm/earliest 4.30 am).
You can check the gate also on the website since I´ve just seen they do differ depending on arrival time. Lounges: British Airways/ AIR France/ Lufthansa will close latest 9.30 pm (see website/at the airport/lounges)
Talking about the website:
Berlin-Airports-Eng
Be sure to always choose the "Tegel"-tab for detailled information.
In case your parents get bored: there is an express bus into town and back (bus TXL) for only a few euros and 35 minutes ride each way. you could see even some sights on the ride!
Bee