1) Can text inside a note have character attributes like size, family,Yes! I think you are allowed to put everything inside a note inset. It's just a kind of container. If this is not true then let's change the behavior of note insets.
series, color, ... which are visually formatted? [sorry, I'm behind a text line here, cannot start up CVS LyX]
2) Can you insert a figure or a table etc. into a note?And note insets have already a (yellow) background color. It should be quite easy to adopt note insets for your purposes.
Your solution would allow the opening and closing of *all* notes with the same "branch value", allowing the showing on-screen of, e.g., the German language version... that would be *very* useful.
Michael