1) No, PKHeX is not outdated for Gen 6 and 7. I could still use it with no problem on my part.
2) One thing to note: some moves from Gen 7 are absent in Gen 8, like Hidden Power, Frustration, and Return. You can find the full list here. You won't get banned even if you use them in-game, as you can't. The game will tell you that you can't use those moves in battle. Pokémon from older games can't be used for online battles, either. You have to apply them the battle mark, given at the Battle Tower in Wyndon.
I suggest instead of drag-and-drop, just use Pokémon Bank and Pokémon HOME, especially if you're unsure of how transfers work. You may pay up to $5 but hey, your Pokémon will be all transferred correctly. Pokémon HOME attaches HOME tracker among other things it do to convert it into a Gen 8 Pokémon. That might be the problem of your drag-and-drop, the absence of HOME tracker.