Org-mode has all of this. Non-proprietary? Easy capture? Indexing? Search? Agenda? Mobile-capture and sync? Org-drill for spaced repetition? Integration with snippet capture in browser?
Every single one checked.
Every single one checked.
How do you do the indexing part?
I haven't seen any plugin to do audio recording from Emacs, but it should be easy (if you're willing to dig into elisp a bit; it's not hard) to invoke any kind of CLI tool for that, and then a/ move the output recording to a proper place, and b/ capture the link for org-mode.
> And do quick drawings with a stylus on the screen?
There are picture-mode and artist-mode in Emacs for that, but I haven't tested any of them with a stylus and a touchscreen, and draw in text mode.
As for videos, I don't recall Emacs being able to play them directly, but you can easily invoke an external player.