Do you have any documentation showing there is no difference between debt and equity in determining if an investment is a security?  

So make sure to have those things taken care of.Here's HUD's inspection checklist which would be good to review and keep in mind. https://www.hud.gov/sites/dfiles/OCHCO/documents/52580.PDF 

But then two of the investors I worked with analyzing this deal discovered an engrossing revelation…Included in the documentation letter contained an appraisal report assessing the property at $610,000.00!!

Typically DSCR is minimum 20-25% down, they will utilize a proportion of the current or proposed rental income to qualify.I'd have a second look at the income for full documentation qualification as well..there might be some other ways to qualify income..including asset depletion..

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

These programs should all be full document that look at both the property + you financially. 

It is pretty standard for loan documents to be 100's of pages, so you'll get the hang of it once you find a good/credible lender and gain experience.

In this day and age, not having a online Prescence and clearly documented track record is just a huge red flag

They will also require an unexpired passport and bank documents converted to English if not already in the language and foreign currency converted to U.S. dollars.

From my perspective, they've documented that they are in violation of Colorado law by defining this "fee" as the equivalent of "three months' rent."