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.
What is the ruling on one who sees moisture on his clothes and doubts whether it is semen or pre-seminal fluid (madhy)?
Whoever finds moisture upon waking from sleep and doubts whether it is semen or madhy, and cannot distinguish between them, he may choose between them and act according to his choice. If he wishes, he can consider it semen and perform the ritual bath, or consider it madhy, perform ablution, and wash what it has soiled. This is because if he fulfills the requirement of one of them, he is definitively free from it, and the default is his innocence from the other. And Allah the Almighty knows best.
Is it permissible to offer mandatory prayer while sitting?
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. Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.
What is the ruling on fasting the six days of Shawwal?
Fasting the six days of Shawwal is Sunnah. The Prophet ﷺ said: "Whoever fasts Ramadan and then follows it with six days of Shawwal, it is as if they have fasted for a lifetime." [Narrated by Muslim]
This is because fasting one month of Ramadan is rewarded as fasting for ten months, and the six days are equivalent to sixty days, completing a full year of fasting.