The locks that I use also specify to use Alkaline because Lithium can damage the electronics in the lock. 

As long as you don't argue with them or make them mad, you should not experience more than the usual brain damage of getting permits.

The property has been vacant for awhile, and any searches I do brings me back to the damaged/vacant property and no additional info. 

If the oil runs out and results in damage to the system, the tenant will pay for the repair.I also recommend you be clear about this in your written lease for future renters.If there are repeated violations, terminate their lease and start with a new renter.

I would think a rabbit does less damage than a cat or small dog. 

For example, if a family is displaced due to extensive water damage that will take a few months to repair, the insurance company will then look to find temporary housing for their customer/displaced family.

The unit was completely dirty, damaged and looked like a fixer upper.

If you win, they will have to pay the extra expense of the filing fees, etc, on top of what you say your damages are (which would be the cost to hire someone else to complete the job).   

If you have a BAD tenant experience on this property as a rental and lose several months of rent and incur substantial tenant damage that is all coming out of pocket whereas if you had even a handful of rentals the performing rentals and the monies budgeted for capex/maintenance/vacancy will carry that sort of loss.

Any suggestions on how to legally put Damage Deposits into a CD to gain interest?