distill: equations in footnote or a pop-up window

[ali-design]

I like distill popup window provided in footnote and cite. I would like to use popup window to annotate part of text (explaining more). This should be done in these places:
(1) in the page left or right sides.
(2) in the footnote.
For (1): Currently I cannot do sides of the page.
For (2): Currently I get ugly format if I add equations (they won't be inline with text), see this image for example:

Can you please provide solutions for both (1) and (2)?