Yes, you can. By default if you create a slider, then a slide and put down a button, it will be exactly in the center. You can see the process here until 4:14:
just in this case a Heading layer was put down, not a Button layer.
These videos can help getting to know the content mode better:
Not necessarily. At the dropdown list of the “Create slide” button: https://smartslider3.helpscoutdocs.com/article/405-slide-manager#create
you could choose the “Create static slide” option. That will create a slide which won’t move while your regular slides will move under it, so if you put a button on that, you will only need one button.