That is the end of Chapter One. Advancing to Chapter Two happens when you pass the rule allowing you to spank the girls yourself. Many say they cannot advance, but the reason is that the rule you want to pass is on page 2 of "Corporal Punishment" section. Go to that page during the Board meeting. You will likely see a rule about stripping girls to their underwear. Look at the bottom of the page, where it says "page 1 of 2" and click there. You will then see the rule you want. Pass it, and get to about 3x the content you already saw.
There wouldn't be, unless you already triggered strip to underwear. Which you could not have, if you haven't even upgraded science facilities. For that one, guessing you either exited computer without actually buying, or did not wait for the delivery. For the chapter advancement, if it worked for the person with issue (and it did) why would post about it not being possible?
The buttons are ok. I can click them. The first one shows blue because the cursor is hovered over it. Both buttons work.
But I figured it out. When it says "I should tell Miss Chang..." you have to click on the screen / or press space, and you get a new entry into the log. Instead, I was just pressing the shut down button of the screen.