If someone regularly fasts the six days of Shawwal, are they obligated to fast them every year?
A person is not obligated to fast the six days of Shawwal every year, even if they have made it a habit. However, someone who regularly performs a good deed should not abandon it as long as they are able.
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 istinja' after urination, and is it done with water and soap or with water only?
Istinja' from urine and stool is obligatory. It is permissible to perform istinja' with water alone, or with toilet paper alone. The best way is with toilet paper then water. If one wishes to suffice with one of them, then water is better. And Allah the Almighty knows best.
Where should a woman following her husband or another man in prayer stand?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If a single woman prays with a man—whether she is his wife or a non-mahram (Ajnabiyyah)—the Sunnah is for her to stand behind the Imam and be shielded by him. If the Imam is leading both a man and a woman, the man should stand to the Imam's right, and the woman should stand behind the male follower (Muqtadi). In this way, she is shielded from the Imam by the male follower and remains at a distance from the follower and his line of sight. And Allah the Exalted knows best.