That means finding as many other agents in the area as possible who can confirm or deny that arrangement.

I had arranged everything with the title Company doing the closing however they did not follow the process (that they acknowledge in writing) to get the funds from the 1031 intermediary.

I've even arranged for both myself and the seller (who should have a relationship with the current tenant) to go meet with the current tenant to inform them the property is being sold and letting the tenant know what your intentions are (to be a very good landlord) and to ask them what their intentions are..Again, best of luck with your REI!!

The amount I receive in rent covers most of my mortgage payments, allowing me to save most of my income which I plan to use for more properties in the (near) future.I haven't set any systems in place to make our arrangement seem formal.

No, you both would not have to live there with this arrangement.

My preference since my reputation with the seller is on the line is if possible to arrange seller financing on both sides.

Forgive me if this questions has been asked, I did search but couldn't find an answer directly related to our situation.
Preface -
My parents owns a lake house on Lake LBJ. The property has 6 bedrooms and can sleep ...

I was just wanting to see if this partnership arrangement sounded fair and or if anyone as any better ideas.   

Ask yourself: why would a landlord do this arrangement with you?

There’s nothing about this arrangement in the Lease that I know of.