For my AT&T/Yahoo email, yes, both IMAP and POP are supported. I use POP on my computer, and it does download and remove from the Yahoo servers. The phone is set up as IMAP only, as I mainly use it just for “new” mail. I do also have a separate IMAP entry in Thunderbird on the computer, and sometimes copy stuff I want always available everywhere into it’s Archive folder.
As for the note about the Outlook ads, that is from Outlook itself. The Yahoo mail app is similar. I don’t regularly use it, but I remember it would show the ad in the middle of your mail, and only after there are 2 or 3 entries. Not sure if it still does that.