Deleting Emails

Is there a quick way to delete emails in blocks, AND make sure they are actually deleted?   I have 15,000 emails and can't seem to get rid of them.   When I mark emails for deletion, they look like they are deleting, but then re-appear.   Or, after I delete about 40 emails, I get a message that says the emails can't be deleted because my trash is full.   Or, I encounter the check mark problem noted below where emails that I don't want deleted get deleted because they get checked.   This is beyond ridiculous.   I am sure this is happening to others, and if so, it has to be an incredible waste of server space.  I would LOVE to delete all extraneous emails, but Cox is making this next to impossible.    Please come up with a solution to this problem.   Thanks!