I've been struggling with a problem for years now: I get easily affected by fictional characters, like sympathising with them. But most of the time, those characters die. If really depresses me and makes me question my sanity?

Personally, that happens to me a lot too, but I read so much, and am so easily distracted, that it never lasts very long. If you get depressed, try to do something exiting that won't remind you of the character. Take your mind off of it, and start a new book. (Or movie or... You get the gist.)