I'm pretty sure C's are set up the same way as B's, on mine, the window needs to be fully down for the gate to drop down.

Tailgate lock is just that. Even if your car has manual locks for the main doors, the tailgate will have a power lock. Its not uncommon for the solenoid in the 'gate to rust up. You don't need it for the gate to swing both ways.

Yes, the window should go down with the key.