Praise be to Allah.
Yes, he should order them to pray, as the Prophet (peace and blessings of Allaah be upon him) said: “Instruct the child to pray when he reaches the age of seven…” (Reported by Abu Dawood in al-Sunan, Kitaab al-salaat, Baab mataa yu’mar al-sabiyyu bi’l-salaat).
The scholars said: “The child should be taught about tahaarah (purity and cleanliness, i.e., wudoo’ etc) and prayer when he reaches the age of ten years.”
The meaning of discipline or instruction is to smack (lightly when and if necessary), threaten and rebuke. The child’s guardian should teach him about tahaarah and salaat (prayer), and tell the child to do these things, when he reaches the age of seven, and he should discipline him and force him to do them when he reaches the age of ten.
The guiding principle here is the hadeeth (narration)of the Prophet (peace and blessings of Allaah be upon him): “Teach the child to pray when he is seven, and smack him (lightly)if he does not pray when he is ten.” (Reported by al-Tirmidhi, who said it is a hasan/sound hadeeth).
According to another report, he said: “Tell the child to pray when he is seven, and smack him (lightly) if he does not do it when he is ten, and separate them in their beds.” This training is ordained by Islam to teach the prayer and let the child get used to praying, so that he will be accustomed to it and will not forget it when he reaches puberty. There is no difference between boys and girls in this matter of discipline. (See Al-Mughni by Ibn Qudaamah, Baab sifat al-salaat).
Some people may not feel comfortable about disciplining orphans, but the right approach is for their guardian to teach them and direct them in whatever way is beneficial, even if this involves being harsh with the child for his own sake. There is nothing wrong with that, as the poet said:
“He was harsh so that they would understand. Let the one who is determined and resolved be harsh sometimes towards those for whom he cares.”
The scholars said: “(A guardian) has the right to (lightly) smack an orphan under his care just as he would (lightly) smack his own child.” (See Al-durr al-mukhtaar: Baab al-ta’zeer).
As regards the matter of an orphan calling his guardian “Father” or “Daddy,” this question has already been answered: please see question # 1041. And Allaah knows best.