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 a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?
It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.
A person vowed to slaughter a sacrificial animal. Is he permitted to eat from it?
If the vowed sacrificial animal was for the sake of Allah, and the one who vowed didn't specify then its meat should be distributed only among the poor and needy similar to distributing Zakah of Al-Fiter so neither him nor his dependents permitted to eat from; however if his vow was to made a banquet and invititing his relatives and others; then he must bring up as much as he can from its meat for them. In addition, he is permitted to eat from it in a reasonable basis. And Allah Knows Best.
Is it permissible to repeat the Istikhara (seeking guidance) prayer, and is it a condition that one should sleep after offering it?
All perfect praise be to Allah,The Lord of The Worlds Istikhara is offered once, but it is permissible to repeat it, and sleeping after offering it is not a condition for its validity. And Allah Knows Best.