Carla, two answers!
First, if you really want to delete PMs, first, mark them. Then go down to the very bottom of the PM page and at lower right you'll see a box with something like "mark/unmark all messages." If you click that, it will open up a menu with other choices, one of which is "delete all marked." Choose that, then click the "go" button and they'll be gone.
Also, though, you don't have to worry too much. When your box gets to be 100 percent full, nothing bad will happen, except that at that point the oldest messages in your box will begin to disappear, starting with the oldest. Unless you're really attached to some very old messages, you can just ignore this. But if you do want to curate them, then go back to no. 1.
Also, it's fine to ask in this forum. Not restaurant-related, but forum-related, so it's all good.