Is there a way to get an e-mail-notification on questions I marked as favourite but which are not my own?
Or am I using this favourite-mark-system in a wrong way?
That is not possible (as far as I know). However changes in favorites will show up in the pop-up when you hover the mouse over your name on the top bar.
If you're particularly interested in specific questions, you could retrieve their RSS Feed URLs, e.g. https://tex.stackexchange.com/feeds/question/32911 (→ the post number), and subscribe to e-mail notifications for them via an external service, e.g. http://informant.se/ (with which I have no experience, you can find a bunch of them via simple googling). This is, of course, far from getting notifications for all favorites automatically.
Online automation scripting pros might find some way of automatically extracting all the post numbers of your favorites and adding them to one of these services, but that is far beyond my knowledge.