An Agent can propose a tenant as an option but you should do your own due diligence to screen said tenant.

"A city proposal to require tracking of municipal and commercial energy use has the potential to help city government, private building owners and tenants save millions of dollars, reduce emissions by thousands of tons and cut water usage by billions of gallons in less than a decade."

Mario, you need to see what your friend is looking for, or offer them a proposal. 

How do you propose a lower price than listed?

Getting your first rehab project will require you to create a SOW, talk to contractors, compare and review bid proposals, review budgets, & make countless trips to Home Depot.​You will inevitably make mistakes and underestimate things, but you will learn 90% of what you know by just doing your first rehab!

How sure are you that the new realtor's proposed list price' is accurate?

From NOLO:Amount of Notice Connecticut Landlords Must Give Tenants to Increase RentConnecticut landlords are not required to give a particular amount of notice of a proposed rent increase unless prior notice was previously agreed upon.

The $500k cap has been proposed, I doubt it will happen - there's just not the political will.

In the scenario you are proposing, you are the one with the mortgage and the other partner now has partial control over the property.

Checkout TLDR below.I recently came across this article where I read about California's proposed subsidy for housing purchase. https://www.businessinsider.com/california-dream-for-all-program-senate-democrats-new-home-costs-2021-6.