@Cynthia746 I'm sorry that you've found yourself in this frightening situation. I would encourage you to maintain contact with the police, change your locks, and temporarily stay elsewhere if you feel you are in immediate danger. If any of these steps affect your upcoming bookings, contact these guests right away to prepare them for any possible disruptions of service.
When you feel that you're in a safe situation, it's time to re-evaluate your expectations of Airbnb. It's important to realize that renting a home to strangers off the internet is a high-risk enterprise - most of the "trust and safety" that Airbnb advertises is just marketing, and in practice it's fictional. Airbnb does not conduct background checks on new profiles - anyone can set a profile up with a fake name and have a confirmed booking in a matter of minutes. Most importantly here, Airbnb is not "sending" you guests - rather, your listing is posted in full view of anyone with an internet connection, and they decide of their own free will where they want to book. You have some means at your disposal to screen guests - for example, if you haven't done so already please make sure Instant Book is deactivated so that guests have to send a request in order to book, so that you can correspond with them before making a decision.
Another thing you will have to consider if you want to continue hosting - no matter how you feel about it, Airbnb is not responsible for your safety. They are a listing service, they are responsible for hosting your web content and managing payments, but there is no realistic way that a bunch of IT workers in San Francisco or call-center operators abroad can look after your safety and well-being on the ground level. You as the host are fully responsible for securing your property, insuring your valuables, screening your guests, and also for defending your home and removing trespassers if it comes to that. These are not services offered by Airbnb - their entire business model assumes that property owners are the ones bearing the burden of risk, and you have to decide for yourself whether this is something you are comfortable with. Another thing you should know, as it's not really clear, is that Airbnb does not charge guests a deposit for damages even if you specify one in your listing (that's a placebo, don't be fooled). If a guest damages or destroys your home, you are completely at the mercy of the person in an Airbnb call center and your own insurance provider to receive any compensation.
I wish I had more encouraging information here, but when it's your home at stake it's very important that you understand clearly what you're getting into before the worst can happen. It's not clear to me whether your reaction to the guest was justified, if the only cause of your concerns was a criminal conviction from over two decades ago. Perhaps there were other behaviors that made you feel unsafe, but you will find that even a guest with zero criminal record will become agitated if you treat them as unwelcome when they've done nothing wrong. An Airbnb host in a major city will get bookings from all over the world, and you don't get to discriminate against people from countries that don't put criminal record data online. So if background checks are important to you, long-term tenants or a property management company might relieve some of your uncertainty.
