Offices pretty much except for a few business models you can use space anywhere.   

I presume that's vital information to know, right?

There is an exception for lease-options for 180 days or less under Sec. 5.062(c) – otherwise, the residential sales contract promulgated by TREC would violate this provision when combined with a temporary lease.

He wants to partner with us - him being the financial partner and us being the managing/landlord partner, owning a rental unit together.This sounds like a good idea except the worry of the potential for family problems that can happen when money comes in the picture which I would hope wouldn't be an issue.

Ineligible Transactions The following transaction types are not eligible as cash-out refinances: The subject property was purchased by the borrower within the six months preceding the application for new financing except if delayed financing guidelines are met.

Though exceptions can be found or developed, I would suggest assuming that risk and return are commensurate. 

I agree with Jeff, except it seems, according to your example, that your outstanding mortgage would only be $80,000 (since you put $20k down.).

Ineligible Transactions The following transaction types are not eligible as cash-out refinances: The subject property was purchased by the borrower within the six months preceding the application for new financing except if delayed financing guidelines are met.

Are they any ways to get exceptions to this rule?  

I don't have much to bring to the table except for a willingness to learn.