While there's nothing in the contract that stipulates this, we agreed to do so based on our good faith.

The lease does stipulate that if they don't want to renew a lease, or want to leave after going month-to-month at the end of a lease, they need to give 60 days notice. 

If you do not have such a clause in your lease, you need to have tenant sign a new lease stating it's m2m and in which you stipulate the (increased) monthly rent amount.

Essentially it stipulates that they will assess the risks of back flow at my property and determine whether or not a back flow prevention device is required.  

In the lease there should be some stipulations about noise/nuisance to the area.

What are the legal stipulations for that?

My HM lender gave me a proof of funds letter with the stipulations spelled out.

The banks may not consider your offer as seriously if you are getting conventional financing, but there is absolutely no rule that states that you can't get a traditional loan against an REO.As for inspecting the property, my guess is that the bank is stipulating that you have no "due diligence period" after the contract is signed.

If your using a REALTOR contract, then you need to make an addendum that stipulates your requirements for a title free of any restrictions.

That will depend upon your contracts.You should have okeyed the contract for rental OR supplied one to the PM for your renters and that contract stipulates what happens under this or that situation.Also you have a contract with your PM company which stipulates what they can do or authorize as far as renters, deposits, ect.Anything not covered in the rental agreements and or the PM agreement should be okeyed by you before it is done.