They are going to do pretty much the same what I am doing right now (which is posting on Zillow and similar sites and putting a board in front of the property) as long as it is about renting.   

We used to charge an extra refundable pet deposit added to normal deposit for a pet, but once the ESA online thing got so ridiculous, we just raised our security deposit requirement across the board so we're more protected even if someone has an ESA or tries to get an ESA once they move in.

I have a remodel, built in late 1950s that has cement board with holes in it then plaster over top of that. 

However, when I told the tenant that I will provide one hotel suite for 4 people (2 queen bed with kitchen and free breakfast), she has started demanding me to provide room and board for everyone including the dogs.

So today ozone treatment and air return box repair, then I found some dry but soft base board behind the refrigerator

My pleasure, I would have loved to help more, but I have been working really hard to get more of our bigger national banks on board with rural properties but the appetite is just not there for some reason. 

There’s usually a one-time per loan fee for boarding (approximately $50) and if you decide to leave the servicer or take back a particular loan, there’s usually a $50 (approximately) one-time fee for “de-boarding” the loan.Skip Tracing – Servicer will research many different avenues to try to find your borrower.

She proceeded to fill the entire common entry space with decor, message boards, side tables etc.

She is thinking of renting out her house for short term rental while she's gone to make up for some of the costs of being gone (she has some special need dogs that cost more to board).

Yes, you probably will need to get permission from the HOA board or a specific rule change.