So when I have someone coming from, say most recent was Brazil, I ask for supporting documentation from his home country.

Just be prepared to provide documentation, such as leases or bank statements, to verify the rental income.

Bring your documents,  TIN, and a check to deposit into the account and most banks open them for our clients.

Hiring an attorney to look at the documents is a good idea but doesn't come cheap.I would recommend googling things along the lines of "Evaluating passive real estate syndications."

Make sure the CCRs/ governing documents do not put limitations on use.

Are there any other documents I should ask for?

Also, you and tenant would not have to print, sign, and scan the document every time. 

I do all tenant relations and use Adobe sign for all documents. 80% of my tenants pay electronically and no one has been late.

In my life outside of real estate, I worked in Information technology where I have participated in the creation of open source software as well as documentation published under creative commons. lots of license thinking to borrow from.It has always felt wrong to attempt to monetize everything associated with real estate investing.

However, since you’re buying into a shared building, it’s equally important to request maintenance records and financial documents from the condo association.