The usual reason that such folders can't be deleted is because the email provider prefers them. You might first check your online account first to see if the folders can be deleted. If so, you could then replace with a different name, although the email provider might switch it back.

You make a folder the designated folder for storing sent messages in Account Settings > Copies & Folders.

"sent mail" and "sent" subfolders

You're seeing those as subfolders of what? Post a screenshot of what you're observing, please.