Kenzer,
To your first question about liability, yes a LLC can help protect your assets from taken, but you have to manage it correctly. I recommend that you contact a lawyer to setup this process for you. You will want to transfer the deed for the home to the LLC. You might even want to setup a C-Corp (for tax and liability reasons as well) to manage the business with the guests and pay rent to your LLC. This is a bit more involved, but as you scale, it is something you should consider.
In response to your second question, I would say "yes" to allowing pets. They are coming to your property if you allow them or not (you cannot forbid service animals)
Consider the facts: https://www.dogster.com/statistics/pet-travel-statistics-tre....
Top 12 Pet Travel Statistics
78% of American pet owners travel with their pets each year.
54% of cat and dog owners plan to travel with their pet.
58% of people would prefer to travel with their pet over a friend or family member.
52% of travelers base their travel plans on accommodating pets.
About 75% of luxury, mid-scale, and economy hotels allow pets.
In 2019, a total of 404,556 animals were transported by airline.
Nearly 64% of travelers prefer to travel with pets by car.
42.9% of people look for a destination with hiking and fresh air for pet travel.
Dogs make up 58% of the pets traveling around the world.
37% of owners take shorter vacations because of their pets.
10% of travelers have hidden their dogs to travel.
27% of dog owners go the extra mile for their pets.
