Many or all the the units may already have signed leases, but every time we purchase an apartment building we give every tenant a copy of our lease even if they don't sign it so the tenants know our House Rules, how we start the eviction process when their rent is late, who to contact when they have any issues, etc.When we purchase a property we always write a letter introducing ourselves.

If the system is looking at the same 100 properties as comps for both myself and the housing authority, my estimate might be based on the average for some or all of those properties, without regards to any amenities, but the housing authority's estimate is going to extract a narrower set of values, rendering a far more accurate estimate.

The blunt instrument of using one’s net worth seems woefully inadequate and is designed to serve the bureaucrats providing oversight.

Normally as @Craig Yarnell said you finance one way to purchase the property and then after a period of "Seasoning" you refinance to get most or all of your money out. 

So going back to the example of a rental property held in a land trust, the beneficiary may receive some or all of the rental income, depending on the terms laid out by the grantor.As the grantor of a land trust, you can change its terms at any time.

If your new Primary Residence will be bought with a Conventional loan, you will MOST LIKELY only need a lease agreement from your departing residence in order to count rental income and offset some or all of the mortgage payment for that departing residence.

If you do it right, you can defer or offset most or all of your tax from a syndication. 

The hard part is finding a 2–4-unit property that will allow you to live in one unit while having the others cover most or all of your mortgage payment.

Bergford, 12 F.3d at 169.This should be satisfied: (Main Points)The co-ownership may not file a partnership or corporate tax return, conduct business under a common name, execute an agreement identifying any or all of the co-owners as partners, shareholders, or members of a business entity, or otherwise hold itself out as a partnership or other form of business entity (nor may the co-owners hold themselves out as partners, shareholders, or members of a business entity).

There are a number of programs offered by lenders which may be able to help with part or all of your ask.