Does Laylat al-Qadr move between the nights of Ramadan?
Laylat al-Qadr is definitely in Ramadan, and it is most likely in the last ten nights, especially on the odd-numbered nights.
For this reason, the Prophet ﷺ commanded observing worship in the last ten nights, and he himself used to dedicate those nights to worship. Many people put special effort into the 27th night of Ramadan, and they are rewarded in any case, whether they actually coincide with Laylat al-Qadr or not, because worshiping on any night of Ramadan carries great rewards.
What is the ruling of Islamic Law on one who died owing debts and left no wealth? Is it obligatory upon the heirs to settle these debts?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The general rule is that if a person dies owing rights to other people, such as debts, these are settled from his estate, if he left any wealth, before the estate is divided. The Prophet (peace and blessings be upon him) said: “The believer's soul is suspended by his debt until it is settled for him.” Graded ḥasan by al-Tirmidhī. Repayment of debts takes precedence over the heirs’ right to inheritance.
If the deceased left no estate, or left wealth that was insufficient to cover his debts, it is not obligatory for the heirs to pay from their own wealth, but it is recommended for them to do so, because the deceased’s dhimmah (legal liability) remains occupied by the debt. It is reported in some narrations that he remains held in suspension until his debt is paid, and it is not part of filial righteousness for a child to leave his father’s dhimmah burdened with debt.
All of the children may contribute to settling the debt on behalf of their father and cooperate in doing so, even in installments, according to their ability. And Allah Almighty knows best.
When is Istikharah (guidance prayer) Du`a offered, before Tasleem (saying asalamu alikum warahmatu allah wa barakatuh to end the prayer), or after it?
It is offered after Tasleem.
What is the ruling on preparing food for someone who is not fasting in Ramadan?
It is forbidden to prepare food for someone who is breaking their fast without a valid excuse in Ramadan.
Doing so would be assisting in sin, and assisting in sin is itself a sin.
Allah says {what means}: "but help ye not one another in sin and rancour" [Al-Mai`dah/2]