Some have a deeper lower cabinets depending on clearances.This apartment was occupied by a young couple on welfare (he worked off the books) who always paid on-time etc but smoked inside for many years before we took possession.

Change your mindset to getting the property back in your possession as soon as possible. 

I asked him, “Have you ever not paid anyone and forced them to take possession of a property.”

But I also have no way of knowing if they would, out of the blue, file an adverse possession claim of the portion of our land on "their side" of the fence, which I guess we all believed to be their property.

This seems like a risky deal, but a good one because there's someone who might have some title to the land who wants me to have it, the quit claim deed is so cheap and there are no back taxes.Note: I do not have enough capital to fund a construction project immediately, but I could start the adverse possession statute of limitations by fencing and clearing the lot.What am I missing?

Your other example is an unlikely situation but had you made such an agreement, it would likely be just an extended escrow period with your possession at close of escrow so long as you performed on those specific terms with seller. 

Our local adverse possession expert Rick H. hopefully will chime in. 

Generally, realtors go in with credentials that an average, unlicensed person, does not possess.

In fact, often “fast cash” gets construed to be expensive, but if you’re receiving “fast cash” through the sell of an item that’s constantly and forever losing value, it’s more cost effective the sooner you sell it for fair market value.People get mesmerized by the big numbers involved in real estate and how unattainable those numbers seem, but then fail to put into perspective what percentage of our luxury belongings and expenses truly are in comparison and what could have happened if we designated those funds into investments instead of material possessions.- The $2000 TV hanging on the wall…that’s 4% of a $50,000 property that around my town in central Iowa will buy a basic, move in ready, two bedroom bungalow.- A $4000 credit card balance someone racked up from the past six months of excessive shopping and entertainment…a whopping 8% of a $50,000 home.- That $6,000 family vacation to Disney World is a staggering 12% of a $50,000 property.- The $12,000 boat sitting in the neighbor’s garage he only takes out 4 times each summer, it is basically a 24% down payment for a mortgage on a $50,000 rental property.Heck, even the PS4 that I just had to have for some late night Call of Duty action and spent probably $700 on including a couple games and accessories is just a hair under 2% of the total $36,000 purchase price of the investment home I bought – and I actually find that sort of sickeningly interesting if you really put that into perspective.

Finally, I am certain a lender would not underwrite a mortgage on the property if they possessed knowledge of the present use.My advice, for what it is worth, would be to consider moving into a better living arrangement and under no circumstance consider purchasing this problem from the current owner.