I heard a Hadith about people gettting punished in the grave for missing Fajr (The punishment is being struck with a rock to the head) but I just wanted to know if this Hadith is authentic and if it was, would we get punished even if we make it up once we wake up?
Sleep is considered a legitimate excuse for missing prayer:
"They asked the Prophet about when they slept past the Salat. He said: 'There is no negligence in sleep, negligence is only while one is awake. So when one of you forgets a Salat, or sleeps through it, then let him pray it when he remembers it.'" (Tirmidhi)
So, as long as you had the intention to wake up and pray, there should be no sin on you God-willing.