Most likely, an insurance company is going to want the address to be verifiable before they offer coverage. If the unit doesn't have an address, you should list the main residence's address on your renters insurance and the same rules would likely apply.
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.
Typically, your renter's policy will not cover your hotel due to your air conditioner being out. A broken AC is not considered the loss of use of the dwelling (home) — they typically only pay for other accommodations when the entire dwelling is uninhabitable.
LexisNexis is the company that maintains the insurance claim database. If you are disputing a claim, especially if you're the victim of identity theft and you did not file it, you should contact them about getting it removed.
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.
Your renter's insurance policy only covers your personal property and personal liability - not the property or displacement due to an issue with the dwelling. Since it is an issue with the dwelling, your landlord should have coverage for this type of issue on their policy.