I was looking through some listings on Propstream and found a house that has reached the "Notice of Trustee's Sale" stage of pre-foreclosure but it shows it was purchased in cash so there is no mortgage on the property. 

It would be a nightmare for the seller to have to give multiple 24-hour notices to enter tenants' apartments for people who are not serious about buying the property and it would be very time-consuming for the sellers, tenants and brokers.

But a basic like a rent increase with proper notice should not be negotiated.I would not explain in detail as they will just counter whatever you say. 

I noticed the Est Mortgage on BP is always $100-$200 off compared to the MLS.

When I have rented to folks in this situation, it's one lease that everyone signs (and everyone gets a copy), tenants are responsible for setting up and paying the utilities, the lease CLEARLY states no additional folks can reside there (it's not unusual to have boyfriends/girlfriends/friends who have been kicked out by parents or lost their rentals show up and start living on a couch) and an early buyout clause in the lease (typically 30 days notice and two months worth of rent) since sometimes these type of situations do not work out. 

@Nathan KapustaI would resend that notice.

The water heater had a little corrosion, which I saw (and frankly means it needs to be replaced) and he said one previous inspector noticed a little condensation in the electric panel.

Or serve him 30 day notice and let him know we’re not renewing his lease?

I've noticed that the mortgage amount on BiggerPockets is always lower than number generated by https://www.mortgagecalculator.com . 

I noticed this happened because in my analysis I was putting 3.5% down payment (FHA loan) which would increase the monthly mortgage since I am putting a little up front.