If I carry the fight, I can get injured or maybe the fighter I am facing gets a lucky punch.

I was thinking along the lines of someone being injured on the property or any other situation that I can't imagine.2.

But I suspect it was for personal injury because he fell and injured himself once when he was alone in the apartment, and drunk and feeling dizzy. 

If you lie, that could open you up to future liability; if you tell the truth, that could limit your buyer pool (a lot of people don't want to buy a house if work wasn't permitted);-  Worst case, down the road, if there is a defect in workmanship that results in someone getting injured or killed (electrical fire or gas leak, for example), you could potentially be held criminally liable and/or find yourself getting sued.

On August 4, the tenant stated they were involved in a shooting and got injured and provided all evidence supporting this claim. 4.

The claim was because a neighbor was injured on my property and had $2800 in medical bills. 

She said we're lucky she was not injured (has since mentioned this 3 times).When the handyman reached out to schedule a time to come evaluate and estimate (we live out of state), she texted him a dozen times with measurements and instructions about what he needed to do.

There is almost no reason your property is going to be sued where you will not also be sued personally as you probably made the decision that caused the other party to be injured. 

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

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