Is it permissible for the man to go out wearing shorts?

All Perfect Praise is due to Allah, The Lord of The Worlds

It is permissible so long as his Awrah (private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed. And Allah Knows Best

How does a praying person prostrate?

All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                                        It is from Sunnah that he/she sits with both knees on the ground in order to prostrate, then hands, nose and forehead are placed on the same place. In addition, the toes have to touch the ground, and be directed towards the Qiblah (direction of Ka`bah) during prostration. And Allah Knows Best.

Is it permissible for a person who broke fasting in Ramadan because of being sick to pay a ransom?

If there is hope for him/her to be cured, then he would be required to make up for the missed fasting days when he/she recovers, and no ransom is due on him/her. If his/her disease is incurable, then he/she would be required to pay a ransom for each missed fasting day, which is (600) grams of wheat, or rice. And Allah Knows Best.

Should the father command his ten-year-old daughter to wear the Islamic dress?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

The father should order his daughter to put on the Islamic dress once she turns ten, in order for her to get used to it. And Allah Knows Best.