The 2nd "que" is not necessary. It's used in informal situations. Formally it would be "O que ele disse?" and "O que você fez ontem?" In my opnion "Tu fizeste" is not too much usefull. It's not wrong, ok? But, we portuguese native speakers don't use sentences like this on our day-by-day.
About "O que é ele disse"... This one would be wrong, because there is that "é", and you know what? When you use this "é" in these situations you'll need to use the other "que". Hahah If it got you confused, just talk with me. Hahah I'll try to help ya. You can practice with me anytime you want. Sorry if I wrote something wrong. Just lemme know about it. hahah Xoxoxo