In relation to the Feynman Lectures on Physics and his own works, Edward Tuft notes in response to Sidenotes v Footnotes:
[T]here needs to be worthwhile material that naturally belongs in the margin. If the marginal materials are simply references, then the standard footnotes (at the bottom of each page, not ganged together at the end of the document) are fine. Maybe the empty space in the margin can be left for marginal notes written by the readers, if any.
Earlier on, he also points out that the page width dictated the use of the two-column format, simply because 8.5 inch page width "is too wide for a single column of type; thus 2 columns of text are often used in books with an 8.5 inch page width. In general, a line of text should not be more than 2 or 3 alphabets long, unless there is spacious leading."
So, it would appear that the use of margins had more to do with the size of the page and making sure lines of text were not too long than any sort of requirement to leave space for readers to make notes.
Therefore, in relation to your first question, I would defer to Tuft's reasoning: default to footnotes if your materials are simply references. If they're not, then I would suggest usage of side-notes would make sense instead of footnotes.
Using both together may be necessary if you have a large number of notes, or limited margin space, or even if the places where the notes exist mean that placing them in the margin would cause potential issues. Your example lecture notes has a good illustration of this on page 6, where points 4 and 5 are located on the same line. Note that side notes are (for the most part) not numbered, because they are parallel to the text in question. Placing them in the margin would have caused issues since they refer to the same line.
You could also try make a distinction between footnote material and side note material, and this leads into your second question. I would suggest the following: side notes are exceptionally useful to provide some information that helps explain extra information without the reader having to scroll to the bottom of the page and then back again. It only makes sense if you've got the space for it, and it improves legibility, rather than hinders it.
A good example is something like a very specific technical word definition, or symbol definition (both of which your example of lecture notes does). Your lecture notes example seems to adhere to this for the most part, but it's not a hard and fast rule. If anything, what to put where seems to be dictated by expedience: length of the note, size of the printed page, placement of the note, the type of note etc.
My personal preference would be to choose side notes (print format permitting) for those cases where there is very useful, extra information to elaborate on what's being read that the reader should know, while footnotes are left for those cases where there's a reference, the sidenote would have been too long, there were too many side notes which hindered legibility, or the information itself is something that the reader may need, but is not necessary for overall understanding of the subject. However, like I say, the underlying criteria seems to be more related to the print format, and experience, than anything else.