Whoa, wall of text. Space out your posts, dang!
It sounds like you're affected by the second ban, the one related to game sync (Wonder-guard Arcanine tipped me off).
Going to answer your post part by part.
For starters, I'm not sure if traded Pokemon won't get you banned.
I would tell you not to risk it, but if you have to, OT, TID, SID of traded Pokemon would be different from your main save (for obvious reasons),
and your save's trainer's name would be the Latest NotOT Handler.
If it's legal, Pokemon Bank would accept it.
My National Dex in Pokemon Bank and in Sun Moon (the game does record what you have seen and obtained, just doesn't display it)
is complete with all possible Pokemon, and I ain't banned (yet)
Just in case I haven't mentioned it (I feel like I have, in the other thread),
we don't know the specifics of how one gets banned.
(it's not like we work for Game Freak, and it's not like they listed out clearly what leads to people getting banned)
It is possible that once you game synced, they may compare before and after saves (on their server), against other variables in the save that we have yet to document,
to see if you legitimately obtained everything.
No one will be able to give you a definite answer and no one will be responsible for you being banned, if you still somehow got banned.
I don't use PKHeX on my main cart, and I trade over whatever items I need for my personal game play, as I know trades count are logged.
PKHeX does tons of things, and that's one of it.