Should I keep the 'front static page' blank?
It's up to you. You can leave it blank, so it displays only the slider, or you can add some content (a welcome message, an intro to the site, or whatever you see fit for for your homepage).
The first home slider image is the only one working. How do I enable all three that I would like to rotate through?
I cannot know what you didn't do. Maybe you didn't select three pages in Appearance > Customize > Home Slider, or you didn't set a featured image to the two of them, or the featured image isn't large enough.
When I click on the title of the page in the bottom right of the image where the '>' arrow is, the featured image shows up again below
That's because you selected the Home template for that page (so the page is also displaying the slider). Only the page you've set as your front should be assigned the Home template: the other pages should be assigned the default template.