Note, you don't "Take over" the mortgage typically, you just pay as the successor once you legitimately establish yourself as the successor (Will, Trust, Court Order).

But I cannot find a regulation or law anywhere compelling this. 

There are programs that let you buy an investment home as an resident alien, or Foreign National.You can focus on a DSCR program but in most cases need to have a credit score established best to be above 720.

First, establish an online presence and join local groups and orgs to get your name out.

Entirely different class and many rules and regulations will have to be followed to maintain commercial units.

Is there any benefit to establishing a “parent” LLC that would own the separate property LLCs?

While I understand regulations may vary by condo association, I'm also wondering if there are general restrictions on operating Airbnb in the area. 

Six Areas of Focus:Florence OR - Proposed regulation but nothing formal yet..within city limits properties are eligible for STR usages with a business license to remit local occupancy taxes. 

In this type of deed, the seller does not guarantee that their title is free and clear of any defects before the seller acquired the title or ownership of the property.A special warranty deed generally contains this similar clause:“Grantor does hereby bind Grantor and Grantor’s heirs and legal representatives to WARRANT AND FOREVER DEFEND all and singular the Property, subject to the matters set forth in this Special Warranty Deed, unto Grantee and Grantee’s heirs, legal representatives, and assigns, against every person whomsoever lawfully claiming or to claim the same or any part thereof, by, through or under Grantor, but not otherwise.”Quit Claim DeedQuite contrary to general warranty deed and special warranty deed, a quit claim deed does not establish title of the seller in the property.

Not really, as long as you are up front with a lender, most would just require you to show them the establishment of the LLC/accounts and then could proceed with that.