It was small, but did an adequate job in a big one-bedroom. 

In CA, if a tenant wants to run a daycare in a SFH, the landlord must allow it, but I think the landlord is allowed to require the tenant to get adequate insurance (this does not apply to a unit in a multifamily, according to what I've read). 

The home was previously purchased at an upset sale in 2013, so our title company will only insure with a disclaimer that they won't cover us if the previous owner, who lost the home at a tax sale, comes back and petitions the court to claim the house back saying they were not adequately informed of the back taxes or sale.

I feel like if the plastic underpayment pad is put on properly, it would be adequate protection. 

If not the judge, then certainly a local RE attorney.Also, is there adequate documentation on the part of the seller regarding the non-payment of rent, or could this be a he-said she-said type situation? 

I actually looked up whatever government agency places standards for living conditions and then threatened to report the complex to them for not providing adequate heating.

As long as you entered this investment in adequate financial form, there's no real danger to doing it weekly. 

Sharpened the blades, made sure the rotors turned adequately, but anything more than a fork full of spaghetti meant a total blockage.  

It still has not been able to cool the house adequately. 

Your lease probably states that you have to give the tenant adequate notice to enter the property, and a lockbox would indicate that you are allowing a contractor to enter when they please.