Typically, in our area, the lease gets assigned to the buyer, so buyer and tenant are both bound by the existing lease. 

Potentially gives you the flexibility to do things loosely or more formally.  

Are we bound by this new terms on the contract?

The home is in our names and we have a loose organizational system that consists of receipts/bills in a bill planner (combined with those of our primary residence) and some files in a filing cabinet.

You have got to buy it right, or you could well loose money.Cheers.

Month to month rental agreement, and if it doesn't work, you can give notice without being bound I to a lease.

These loans do not exist anymore.There are several other reasons (bad disclosures, straight fraud, high DTI allowance, and other loose practices etc...) but these are the main 3.

I have an accepted offer one a property in Bound Brook, NJ.

@Joshua Woolls  One can also loose 50k in any market on a flip or buy and hold :)

You have to disclose the lender they may loose 100% of their principal.Ignoring that one of the purposes of a SEC registration is for "registering" with the Gov you as a funds raiser, the main benefit in my view is forcing you to write a Disclosure document that your lenders / partners must sign.