Take the joystick out (or the control panel off) and rotate the joystick around and make sure that the joystick is hitting the diagonals. It sounds like the actuator (the piece at the bottom of th ejoystick that actually touches the microswitch) might be upside down. If you cant hit the diagnols there, you should take the joystick off of the control panel and try again. If its working there then its the whole in the control panel (7/8 should do). If not, its the joystick.
A) Ultimates aren't the ultimate. If you like squared off actuators (so you can feel the corners / direction your pointing) consider buying compititions if you have the ability... BUT I wouldn't do it unless you can return the ultimates.... The comps are better... but only when you can sit them next to each other to test.
If you like smooth circles... Supers are the way to go (on the cheap that is) or 360s (better but cost a lot more and require 5v)
B) Depends on the top. 7/8s should do.
C) Routing is a good thing. But only if you like the height of the joystick on the top. I routed 1/2" in a 3/4. But I like a little space on the top. But this shouldn't effect the courner problems your having... This is really just for the height of the joystick.... But it might help (since the joystick angle is higher... so the end results will be that the whole is a little less defined.
D. I guess yes

Good luck