Not sure if it depends on which mod you want to play. Bounce mods like Xmax don't affect them iirc, but something like Soulvizier might.

No, custom quest or mods won't disable achievements. This game doesn't have that, it might have had in the past but that's not the case anymore. I wish it was an option because sometimes I accidentally unlock achievements I want to get fairly.

Also if you want to ever remove achievements obtained illegitimately, this is what I used: https://www.makeuseof.com/how-to-reset-achievements-for-steam-games/