I am planning to mod my game of Skyrim. However, I have not collected all achievements yet, but I have played a lot of the game by now. I plan on changing the game completely with many mods, though I might do those questlines I have not done yet. I know that achievements will not unlock, but if I were to do it again, with the mods removed, can I still get those Steam achievements, even if the quest was already done while modded?
If you go vanilla with newly created dragonborn and play the questline again then yes, you can get achievements.
However, you can use this mod (link is to Nexus) to unlock achievements while using mods. I'd rather use this mod than go vanilla, I can't play Skyrim without mods...
With SSE Engine Fixes (which you should use anyway) achievements are enabled even when using mods. You can toggle it off if you want but the default is on.
There is no point in also installing "Achievements Mods Enabler".