Can Mini TOC float to the top in "mobile" view (rather than disappear) ?

The next step would be using the browser developer tools to look at the html and css and figure out what styles and properties you need to adjust to get closer to the look you want. Once you find the styles, and figure out the properties, you add those to a custom css file which you add in the User Assets section of the skin.

It can get complicated pretty fast (it's not hard, just brain-bending and overwhelming at first) so if you're not familiar with it, I'd recommend asking a web developer for help.

I don't think there's any way in the interface, although I don't have access to RH2020 right now to check. Assuming you're using frameless, you could have a look by opening the skin, clicking the Mobile icon and checking what options are available under Topic Page > mini-toc. If there're any options, you'd want to try to set the container to display: block.)

If there aren't any options, you might be able to get it to display using javascript, but you'll need a friendly developer to help with that.