If you're looking to get the fees reduced, you'll want to contact an attorney in your area.

With respect to the charge of driving with expired registration...there's nothing to fight. Your registration was expired. Every DMV will tell you that "pending registration" is not the same as a valid registration.

Wouldn't the mall owners have to give permission and supervise the tow?
One would assume that the mall owners have a contract with the towing company. That contract is sufficient permission, and no, they do not need to personally supervise each tow.