osu!standard/taiko/catch/mania have separate skill achievements!
Just play any ranked map with mods enabled such as: SOHRNFHD
Yes, NF mod works. You can find SO mod in "Special" category.
Perfectionist (PF) and Finality (SD) achievements must be used without any other mods.
Packlists can be found HERE. You must pass any mapset difficulty for it to count as CLEARED. You can always check your progress by refreshing beatmap packlist.