I’ve asked for police reports, received nothing, went to the house and found no damage or evidence of forced entry.

Do I take pictures of everything before renting in case there are damages when the lease ends?

That said, assuming no tenant damage (and if it won't net you more rent) I wouldn't renovate if the tenants don't want it.I think the real question is whether the tenants are actually paying market rents.Good luck!

I was thinking of putting the keys in a lockbox and asking the person interested for a copy of their drivers license and Credit card to make sure no damage is done to the property and keys are returned.

If you have no “reserve” capital, it can be nerve racking.  

Now the buyer is being held liable for damages and commissions.

More of a simple screening tool, and at least I have some kind of idea for who to go after if there are damages of fraud. 

I believe the water damage is the root cause of the mold problem, and I’m considering filing an insurance claim to cover the repairs and remediation.For those who have gone through this process, what steps should I take to ensure the claim is handled properly?

Keep at least all those rents added together plus another $20-$30k to cover unseen damage and damage that occurs during move out as well and any required cleaning.

We knew the house would be messy but were not prepared for the extent of the damage.