Managing deleted emails showing up in mailbox other than Trash

I'm not sure what "archive" means here. I usually just either delete emails, or if I want to keep them I move them to a different folder or leave them in the Inbox. My problem stems from when my iPhone settings changed (without my knowing--perhaps with an update) such that swiping left on emails in the inbox no longer deleted emails but archived them, while swiping left deleted them if they were in any other mailbox or folder. Confusing, to say the least. I finally managed to adjust the settings so left swipe was always delete, and then I spent a lot of time going through the "all mail" folder and re-deleting hundreds (thousands?) of old emails. Imagine my surprise to discover they were still in the "Important" folder.

I have never knowingly archived any of them. I never set up this "Important" folder and it doesn't appear in the mailbox settings, nor in the drop-down lists. Here's how my mailbox settings look

Posting this, I just noticed that Trash mailbox is set to none. What? Why isn't it Trash? So I went back into settings and changed it, then set "erase deleted messages" to never, and before my eyes, it changed back to "none" all by itself.

I really don't want to spend more days re-re-deleting thousands of emails. When I delete emails, I want them to go into the trash folder for me to manually empty. I don't want them to go anywhere else. Is this not a permitted combination of settings? Do I need to set Trash to erase its contents after one month?

And back to my main question: If I select the Archive mailbox and activate "erase deleted items", will the items I've never deleted (the ones I want to keep) remain or will they be erased too?