Hi @New19
I wonder if that's your name but hey!
First, try logging out and re-log in to your Airbnb account. Which browser are you using anyway? Google chrome and Safari work fine for me, so far.
Pertaining to a guest who wants to bring in 5 cats to your property, you can avoid such situation by editing your listing. Scroll through you main page and you will see somewhere around the House Rules, there is a checkbox for "pets allowed". Uncheck that box. That way, it is self-explanatory for guests and those who want to bring along pets would not find your listing as they adjust the filters.
Why can't you accept those from your city? There is no button where you can choose your guests' location etc. The only thing you can do is to get guests to send their reservation request to you before confirming. Do not have your Instant Booking on then.
All the best!
Zee