When you check someone, do you have to say "check"? Yesterday I was playing with a friend, I was almost out of time, he checked me, didn't say anything, I didn't see the check as i was in a hurry to make my move. And I was mated.

Computers don't let you play any move when you're in check. Therefore in reality, are you allowed to make a move when you're in check? or you cannot make any move? I mean should you undo any move that you do by mistake or not? And should your opponent warn you about being checked or not?
In a tournament game, you are not supposed to speak at all other than to offer a draw or adjust a piece. This includes saying check. This tends to seep into casual games among more experienced players (I haven't said check in years). 

For players that do not compete in tournaments at all, I don't think that there is any obligation to point it out.

When your opponent makes an illegal move, though, as it sounds like you did after missing the check, it has to be pointed out. You can't just follow it up with a mate immediately. In blitz, making an illegal move means a loss. In a longer game, a minor time adjustment.