no, that is perfectly fine, analogue stick or dpad does not matter (and it is rather a disadvantage anyway, usually easier to get accidental diagonals for example). Only stuff like turbo buttons would be an issue and not be allowed.

I’m not aware of any game where using a control stick is prohibited. But read the rules over first just to be certain.

for NES specifically only thing that could be an issue if your controller allows left+right or up+down at the same time