1. Do you have to "neutralize" the yoke once bank angle is achieved in a wing down landing?
No, unless you want the wing to rise up again due to the secondary effect effect of the rudder you're using to line up with the runway.
2. Will the 777 maintain the (or re acquire the same) bank angle in a gust if the ailerons are kept neutral?
No, unless the gust takes you outside the roll envelope (c.35deg) in which case it will return to 30deg.
3. Is it true that "control inputs must be maintained to displace the flight control surfaces" in a wing down landing?
Yes, if you're doing it properly!
The aileron/flaperon displacement is proportional to control wheel deflection. There is a "gust suppression" function which can command yaw and/or roll but it's for ride comfort and is transparent to the pilot.