Is bleeding that lasts for nine or ten days considered menstruation (Hayd)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the duration of the bleeding does not exceed fifteen days, then all of it is considered menstruation (Hayd), even if the regular cycle ('Adah) has changed. And Allah the Exalted knows best.
What is the ruling of Islamic Law on making up missed voluntary prayers?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is recommended for a Muslim to make up any missed voluntary prayers — whether the regular Sunnah prayers (rawātib), the witr prayer, or his personal devotional routine (wird). As for voluntary prayers that are tied to a specific cause or occasion — such as the eclipse prayers (kusūf and khusūf) — these are not made up once their time has passed.
Shaykh al-Islām Imām al-Nawawī, may Allah have mercy upon him, stated: "The correct view in our school is that making up the regular voluntary prayers is recommended." [Al-Majmūʿ, Vol. 4/P.43] And Allah the Almighty knows best.
Does burping (belching) break the fast?
Burping does not break the fast. However, if anything comes up from the stomach, the fasting person must spit it out and rinse their mouth to cleanse it.
If they swallow it intentionally while being able to expel it, or if they swallow their saliva before rinsing their mouth, their fast is invalidated.
Is it a condition for the mosque where I‘tikaf is performed to hold Jumu‘ah prayers?
No, it is not a condition for the mosque where I‘tikaf is performed to have Jumu‘ah prayers. However, if a person vows to perform continuous I‘tikaf, and Jumu‘ah occurs within that period, then they must observe I‘tikaf in a mosque where Jumu‘ah is held so that they do not break their continuity by leaving for Friday prayer.