So this was driving me nuts and I THINK I was able to solve my sync issue as well as my double bookings issue.
My outlook calendar came first. So to be clear, I'm not trying to add a bookings calendar to outlook. On the syncing issue, specifically, when I blocked off an all day AND set to Busy or OoF, my bookings site was not updating. When I checked my shared calendar setting, it was set to not share with anyone in my organization. I changed the setting to something other than that (I'm the only one in my organization so the specific setting didn't matter). After that it seemed to fix the outlook to bookings syncing issue.
On the double bookings issue, you have to make sure you set up your meetings a "maximum number of attendees" to 1. This defaults your service to 1:1 meeting. If you change the max attendees to 2 or more, it sets up your service as a multi attendee service (e.g. group meeting). Once you create a multi attendee service, the lowest amount you can set is 2. In other words you cannot go back to 1. You have to delete the service and create it again. When you are set up for multi customer meetings, until your customer limit is met, the time stays open. This in theory would allow others to join your group booking which is great if that is what you want. If you're like me and offer virtual consultations in your business, this is a very easy error. When I set up my service I was thinking ahead to being able to add multiple customers to my meetings as sometimes there is more then one person, however all this does it keep your service open until the group booking is full. Setting up the service as a 1:1 meeting and adding additional customers later (if needed) is the method you want to go with.