An injured tenant can only recover against the company.

Unlike my mom in law who is just sick and injured, even if you found the person or their children, they may not be legally make decision to sell.

Years ago I was a town manager when one of our EMT vehicles ran a red light and broadsided a pickup, killing a 15 year old girl and injuring her father.

Is the $2000 savings enough reward if he or his crew injures themselves and sues you?

This could be a maybe for me, but I would check with your insurance company to see if you might be held liable for a visitor getting injured in the pool. 

If someone injures themselves and sues, they will be suing the LLC and not you personally.

That lawsuit is a claim for fraud, and that’s what fraud typically is...a misunderstanding and someone being “injured” and wanting to hold the other responsible for it.

I have big concerns also about injuring any animals with the traps or inadvertedly leaving babies behind.

If someone injures themselves and sues, they will be suing the LLC and not you personally.

You have absolute liability over your real property, which means that if someone is hurt you will be liable for their damages, not having a business practice exclusion in your lease may be presented as negligence in court, with you being a sophisticated landlord/investor/business owner and your renter aswell as the injured daycare student being portaied as victims of your negligence.