@Dana347 In both your Havasu entire home and your Palm Desert private room, you provide sleeping accommodation for way more than the stated number of acceptable guests. Why? If you intend to negotiate and charge for more guests than your listing, you could make that clear in both the description listing and the extra guest fee charged.
In your pre-booking or booking confirmation message, you could request the full names of all the guests. Beef up your rule to read "only registered guests can be on the property" What local presence do you have for the remote house? You would need to inspect what you expect in terms of how the guests use your place.
Regarding your private room listing, it is unclear if there are two bedrooms available as pictured or if only one bedroom is available as labled. Who shares the bathroom? Are you living there or is there another guest room? If each room can be used by different parties, you should list each bedroom separately.