What is the ruling of Islamic Law on a person who abandons prayer after reaching puberty—is he required to make them up?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Making up missed obligatory prayers is an Islamic duty just as performing them in their proper time is obligatory, and taking care of them takes precedence over performing voluntary prayers. This is established by the practice of our Supreme Prophet (peace and blessings be upon him) when the polytheists distracted him on the Day of the Trench from performing the Asr prayer, so he made it up afterward, as well as the Hadith: "Pay Allah what is due to Him, for Allah is most deserving of fulfillment." (Recorded by Al-Bukhari)
Furthermore, it is valid to make up missed prayers at any time.
Whoever has missed a number of prayers and does not know their exact count, it is obligatory upon them to sincerely repent and exert their utmost effort to estimate their number. If they are unable to determine the exact count, they should base it on what is most probable according to their best judgment. They should then make them up gradually; if one performs one missed prayer alongside every current obligatory prayer, the matter becomes easy and manageable, and with the passage of time, one will complete what is owed, Allah willing. And Allah Almighty knows best.
A person prays in a certain spot within the rows of the mosque, and gets angry if someone else prayed at his spot. What is the ruling on this behavior?
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 Prophet Mohammad (PBUH) make it prohibited for a Muslim from having/taking a certain spot in the mosque when performing prayers if they arrived and find it occupied, furthermore; it is the religious duty on others (praying people) to offer a piece of advice to alert the ones who don't know, that whoever reaches a spot first at the mosque having a priority/privilege upon others in that spot. And Allah Knows Best.
Is it permissible for someone with a physically demanding job, such as a baker or construction worker, to break their fast?
It is not permissible for someone with a physically demanding job to start the day intending to break their fast. They must make the intention to fast at night and begin fasting. However, if they reach a point where fasting becomes unbearably difficult, they may break their fast and make up for it later.
Is it permissible for a woman to lead other women in prayer?
Yes, it is permissible for a woman to lead other women in prayer. The most knowledgeable among them in the rulings of prayer should act as the imam. She should stand in the middle of the row, slightly ahead of the others.