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 ruling on water present on the floor of a toilet/bathroom?
The default ruling is the purity of this water present on the bathroom floor. If one is certain or strongly suspects its impurity, then one washes whatever part of the body or clothing this impure water has touched. If one doubts its impurity, the default is purity, and we do not rule it impure based on mere doubt. And Allah the Almighty knows best.
What is the ruling on a Friday sermon in which the khaṭīb did not explicitly exhort the congregation to be conscious of Allah (taqwā) in both sermons, but sufficed with commanding them to obey Allah and refrain from disobeying Him?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
For the Friday sermon (khuṭbat al-Jumʿah) to be valid, certain essential pillars (arkān) must be fulfilled. Among these is the exhortation to be conscious of Allah (waṣiyyah bi-taqwā Allāh), which must be present in both sermons. Alongside this pillar, the praising of Allah (ḥamdallah) and the sending of blessings upon the Messenger of Allah ﷺ are equally required.
Shaykh al-Islām Imām Ibn Ḥajar al-Haytamī, may Allah have mercy upon him, states: "These three are pillars in each of the two sermons, because each sermon is independent and separate from the other." [Tuḥfat al-Muḥtāj,Vol.4/P.447]
It is not a condition that the exhortation be expressed in any specific wording, nor is it required that the word "taqwā" itself be used — such as saying "I exhort you to be conscious of Allah." Rather, this pillar is fulfilled by any expression that contains a command to obey Allah the Almighty and to abstain from what He has prohibited.
Imām al-Khaṭīb al-Sharbīnī, may Allah have mercy upon him, states: "The third pillar is the exhortation to taqwā... The specific wording of this exhortation is not required, according to the most correct view, because the purpose is admonition and the urging of obedience to Allah the Almighty. Therefore, any expression that conveys admonition suffices — whether long or short — such as: 'Obey Allah and be ever mindful of Him.'" [Mughnī al-Muḥtāj,Vol.1/P.550]
Accordingly, what the khaṭīb has done — by commanding obedience to Allah and forbidding disobedience to Him in both sermons — is valid and sufficient. And Allah the Almighty knows best.
What is the ruling on purchasing sacrificial animals and authorizing their slaughter via telephone?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is preferable for the one offering a sacrifice (udhiyah) to slaughter the animal himself, in adherence to the Sunnah, or to be present at the slaughter if possible.
It is valid to authorize a butcher to purchase a sacrificial animal on his behalf and slaughter it, regardless of whether the animal is owned by the butcher or the butcher is acting as an agent in its sale—according to the Hanbali school—provided that the butcher specifically designates and purchases the animal for the person offering the sacrifice before slaughtering it. And Allah Almighty knows best.