How do you remove a mailbox/folder from mail

You must do it from your computer, either using your mail program (if you have one) or using the web client. Mail on the iPad should update after a short while.

If it does not then go to Settings > Mail, Contacts, Calendars > Accounts, and select the account. Turn the mail off using the switch on the right. Close settings and go to Mail to confirm the account is gone. Go back to settings and turn the mail back on.

Go back to Mail. Everything should reset at this point. It might take a few seconds.

This will not effect the contents of any of your folders. It might effect the read status of email in your inbox. It is still a good idea to check your Mail against your computer or web mail before starting. Just make sure everything is in agreement. If everything is good on the computer/web side, then nothing you do on the iPad is going to permanently delete your files.