Are the buttons really free to use?

Yep.

What do I need to use these buttons?

You'll need some kind of web page on the internet where you can post JavaScript code. Tumblr users, for example, can add a button easily. If you run your own Wordpress or other site you're probably able to add the code as well.

Will your back to top buttons work over HTTPS?

Yes!

Is your code based on jQuery or some other platform?

Nope, it's native JavaScript, to keep things light.

Are there any other things I should know?

You can press Shift+T as a shortcut to scroll to the top as well, saving you countless seconds of your life.