If your parents are renters, they are not responsible for the property — just their own liability and possessions — so it's not required to have sinkhole insurance since that's property-related. The landlord has to maintain safe living conditions for their property.
I can't answer this question - you need to look at the exclusions and special coverages in your renters' insurance policy dec page (declaration page). That part of your policy will specify how much coverage you have - if any.
Unfortunately, there usually isn't any coverage provided for contents when you tow something - only for the entity with which you are towing. Meaning, while the trailer would have physical protection extended to it, the contents you were towing would need to be covered by something else.