What is the ruling on seeking forgiveness between the two Friday sermons?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible to seek forgiveness (Istighfar) between the two Friday sermons (Khutbatayn), and it does not invalidate the Friday prayer (Salat al-Jumu'ah). Furthermore, it is not disliked (Makruh) to speak before the sermon, after it, or between the two sermons. Likewise, it is not disliked for one who enters during the sermon to speak if there is a need for it, provided he has not yet taken a place and settled into it. And Allah the Exalted knows best.
Is vomit among the nullifiers of Wudu (ablution)?
Vomit does not nullify Wudu, but it is a Najaasah (impurity) that requires rinsing the mouth and washing whatever became dirty by it since the prayer becomes valid only after the removal of Najaasah. And Allah Knows Best.
Is it a condition for I‘tikaf to be performed in the mosque?
Yes, for I‘tikaf to be valid, it must be performed in a mosque. I‘tikaf is not valid if performed at home or elsewhere.
What is the monetary value for the expiation of an oath (Kaffarat al-Yamin)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The expiation for an oath (Kaffarat al-Yamin) consists of feeding ten (10) needy persons. This is estimated at 600 grams of rice per person. It is also permissible to pay its value in cash, which is estimated at one dinar (per person). And Allah the Exalted knows best.