Restrictions have since loosened but the jury is out on what effect it will have.  

For example a home I was watching went into default, things to that effect were recorded at the county, auction notice, etc, it all showed up there.Then the owner got current.

Other things that can effect value ..... what type of utilities, any capital repairs needed, size, market, upside , vacancy.

Anything by grant Cardone - best one is 10XAlso "The Compound Effect" by Darren Hardy

So you're on the other side of that coin now, and should be giving them one of these.Build that into your interest rate, if you want to effectively have it covered by the borrower. 

It will have no effect on your rents, and would take an act of god to get it moved.

Various electronic rent payments can be set up and they are much more cost-effective than spending, time, fuel, and brain power dealing with paper.  

It is normal for insurance policies to be bound with an effective date of closing or date of auction win and then take a few days or weeks for the actual full policies to be processed and issued.

to see if they publish anything.As licensed agents we grab data from our local MLS and create numerous plots of real estate market trends for sales.

The tenants can clean up their act prior to close or the seller can evict them (though it might take 2 or 3 months) or work through code enforcement (slight danger but better than the current circumstance) to effect the change.