か？、ね？、かな？ are given in my book as hints to the meaning of this grammar point. But the translation I naturally came up with is ‘what was it?’ It’s normally used in conversation when the speaker can’t remember something he or she knows or knew. For example, ‘何だっけ？’ A more polite version is でしたっけ。
絶対に～ないこと。I.e. something which isn’t going to happen. For example: 私は今日レポートを終わりっこない。I definately can’t finish this report today. I haven’t actually heard this used in conversation at all suggesting that maybe it’s not used all that often? Now I’ve studied it, perhaps I’ll pick it up when I’m listening to conversation from now on.