Could take 3-4 weeks just for that depending on the county and their back log. 

Houses on my street just 2 blocks away command at least $150 more in rent.  2) lead paint certs just depend on the property.

When I have already paid my full last months rent does this mean that I am entitled to stay and pay that last months rent, or is the last month pro-rated and refunded depending on when the 30 days ends?

That's a tough question and unfortunately the answer is it really depends.

You may also need to show proof of your down payment and closing costs, depending on how awake the selling agent is.

Depending on the lease you used your document may have a transfer of ownership clause or something similar which requires your consent.If you do not have a personal guarantee or some sort of material change or adverse change provision, I am not sure what recourse you may have with the sale of the business operation.

I too think it is a personal choice that will depend upon where you are in your investment strategy.  

I've looked into Series LLC, and it all depends on what State you are in.  

It all depends on your time frame, but I think if you're planing to hold for 10 plus years you can't go wrong in Denver.

FWIW, it's not particularly easy to get a Green card - although the process can depend on the country of origin.