Bismillah
Curious, just to confirm what Rock said, and i will only address one point.
A beheading sentence according to Islamic Sharia'a is only applied in murder cases when proved.
As for missing prayer, there is not punishment in this world, as the prayer is the right of Allah not a human being. Allah enacted a beheading the murderer because the situation involved the right of another human being including the victim's family who must be consoled in this world, on one hand, and to deter others from committing similar crimes on the other hand. Allah, Is Keen on establishing a safe community as much as possible for us to live in. However, forms of worships are acts that are devoted and performed for Allah and the benefit returns on the devotee (in other words performer). Thus, in such case, why would Allah set a punishment for one who is harming no one but him/herself. This is not logical, given the fact that Allah Is The Wise. Thus, failure to perform worships, is a matter that will be settled in the Day After. However, there are a number of expiations associated with certain worships, such as fasting for instance. Again, on the particular issue of missing prayer, the person is harming him/herself, by missing a golden opportunity that is frequent 5 times a day to meet Allah. Doing so, the damage is all his/hers. A ruler is not charged to enforce a beheading sentence. HOpe I added something.