My goal is to work no more than 40 hours/week at my normal job and still be able to provide for my young family.

These may sell for no more than back taxes.  

What is the city or state law for pets, (usually it's something like no more than 3 per cat, dog etc.

No more needed the houses to be appraised at a certain value to qualify for the loan and no appraisal needed, which could cost few hundred to a thousand dollars.

No more shady than "We buy houses - text your name and number or call 123-456-7890"

Currently I'm interested in trying to qualify for a home loan which would be no more then $80,000.My situation Unemployment 425 a week ($1700 month)I've talked to one bank and they said they'll factor it in the rest none.

That means that your mortgage should be no more than about a half of what your rent would otherwise be, because the property's other expenses will also be about half that rent cost too.But if you DO pay market price, and there IS a down turn, you know where that leaves you?

No more lending so my search continues. 

Meanwhile I am camping out in the house; but since the law specifies the redemption notice to the sheriff has to be filed no more than 30 days in advance, or no less than 2 days in advance, I cannot figure out how much warning I will have that I have lost the house and have to be out on the street (another rich homeless person, how weird!).  

Then, your offer should be NO MORE than that value, less tear down and holding cost, less your own desired profit. ie.