I don't think you can put up a camera for this group if it wasn't mentioned in the listing when she booked.
Is there a friendly neighbor who can alert you if they see more than 4 guests there? And I'd say definitely no to the "friends hanging out". They can hang out at a cafe, bar, park, whatever, they don't need to come into your home. Even if they're not staying the night, they're going to be using up hot water, toilet paper, soap and other amenities, not to mention the security risk for you having unregistered people there, and young ones to boot.