What is the ruling on performing Umrah after the latest expansion of the Mas`aa (the passage between As-Safa and Al-Marwah), is it permissible, or not?
Yes, it is permissible to perform Umrah after the latest expansion of the Sa`y area since making Sa`y between As-Safa and Al- Marwah is already observed. And Allah Knows Best.
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.
What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the 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.