There are examples of all the things you can do on the demo page, and information about all of the classes available in the framework on the documentation pages.
If you are wondering if MooTools is worth a look, and the examples haven't convinced you yet, then take a look at this excelent selector speed comparison between Dojo, JQuery, MooTools and Prototype. MooTools isn't faster than every framework for everything, but is always the fastest framework overall.
Adding a progress bar to the top of the page is a simple way of showing the user how far down the page they have read. There is a scroll bar on the right hand side of the page on my current device, but that isn't always present on all devices.
I was working on a user dashboard recently and decided to add some more signposting to values being updated. Users were able to select different parameters in order to produce different values, but I thought that the values being updated weren't clear enough.
When I first heard the term "Shadow DOM" I had to laugh at the name. I had visions of a cloak and dagger HTML element that would only be seen on the dark web. Or some sort of nefarious shadow site that was the after effect of a hack.