Thanks for a great review!
Re favicons: no, not easily (https://github.com/tborychowski/perfect-home/issues/37#issuecomment-546635708).
I could only show 16x16px favicons, which would look ugly when resized to e.g. 128px.
I'm planning to show more than 1 letter though. Probably something like opera does in their speeddial. Stay tuned!