I underwent a procedure for a molar pregnancy (hydatidiform mole), and after that, the bleeding continued for more than two months, during which I did not pray. Do I need to make up the missed prayers?
If you have previously experienced postpartum bleeding, the duration of the current bleeding is treated the same as your previous postpartum period. Any bleeding that exceeds this duration must be considered irregular bleeding (istihada), and you must make up the missed prayers. If this is the first time, then any bleeding beyond sixty days is considered irregular bleeding. You must perform ghusl, pray, and make up the prayers for the days beyond the sixty-day limit. And Allah Knows Best.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
What is the authenticity of the supplication: "O Allah, bring it upon us with blessings and faith, safety and Islam, and success in what You love and are pleased with. My Lord and your Lord is Allah"?
On the authority of Talhah Ibn Ubayd Allah (may Allah be pleased with him) who reported that the Prophet (PBUH) would say when he saw the crescent moon: "O Allah, let this moon appear over us with blessings and faith, safety and Islam. My Lord and your Lord is Allah."
This was narrated by Tirmidhi (Hadith no. 3451), who said: "It is a Hasan (good) Hadith."
And Allah The Almighty Knows Best.