Ok this is about the registration to the game. Process not complete. Have you verified your War Thunder account via their email?
Once this is completed, the next quest will unlock.
Keep launching the game via Bananatic 'Play' button.
Use different browser maybe if it's getting confused with a previous Wargaming account.
There may be a little delay until you have registered completely to a game. Then quests will appear.
I've completed all these steps, nothing works. I tried it with another account, and it only worked because at the home screen, where you choose a game from the given list, I chose War Thunder, then it asked for my nickname in-game... after I put that in, it began to work, whereas here, it doesn't because during the same process I chose a different game "never" -something...