Can an Udhiyah be made up if its time is missed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the sacrificial animal (udhiyah) is a voluntary (nafl) offering and its prescribed time is missed after the three days of Tashriq have ended, then it is not to be made up as a sacrifice; rather, it becomes merely a sheep for meat.
However, if it was a vowed (nadhr) sacrifice and its time is missed, then it must still be slaughtered, and the slaughtered animal is to be treated as it would have been during its prescribed lawful time. And Allah Almighty knows best.
Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.
What is the ruling of Islamic Law on eating or drinking during the circumambulation?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is disliked (makrūh) to eat or drink during the circumambulation (ṭawāf).
Shaykh al-Islām Imām al-Nawawī states in al-Majmūʿ: "It is disliked to eat or drink during ṭawāf, and the dislikedness of drinking is lighter. Neither of them, nor both together, invalidates the ṭawāf. Al-Shāfiʿī said: 'There is no objection to drinking water during ṭawāf, and I do not consider it sinful; however, I prefer that it be avoided, as refraining from it is more befitting in terms of proper conduct.' Among those who explicitly stated the dislikedness of eating and drinking, and that drinking is the lesser of the two, is the author of al-Ḥāwī."
If, however, a person is in genuine need of drinking, then there is no dislikedness in doing so. In any case, the ṭawāf itself remains valid. And Allah the Almighty knows best.
What is the validity of the formula for sending blessings upon our master Muḥammad ﷺ: *"Allāhumma ṣalli wa sallim wa bārik ‘alā sayyidinā Muḥammad wa ‘alā ālihi, ‘adada kamāli-Llāhi wa kamā yalīqu bikamālihi"* ("O Allah, send blessings, peace, and grace upon our master Muḥammad and his family, by the number of Allah's perfection, and as befits His perfection")?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is permissible to send blessings upon our master, the Prophet ﷺ, using the formula mentioned in the question, since sending blessings upon the Prophet ﷺ is an act of devotion legislated in its basic essence, without a specific prescribed wording required outside of the formal prayer itself. It is therefore valid to perform it outside of prayer using any formula. This particular formula involves multiplying the blessings sent upon the Chosen Prophet ﷺ to the number of the perfections of Allah, the Exalted — which are limitless — so that, by Allah's permission, its reward and benefit never cease.
The meaning of "the number of Allah's perfection" is that it is without limit, making the blessings sent boundless, corresponding to His perfection, Glorified is He, which cannot be enumerated or counted. This formula is analogous to the words of our Greatest Prophet ﷺ, as related in the authentic ḥadīth narrated by Imam Muslim: the Prophet ﷺ said to Sayyidah Juwayriyyah (raḍiyallāhu ‘anhā): "Indeed, I said four phrases after you [left], three times, which, if weighed against everything you have said since this morning, would outweigh them: Subḥān Allāhi wa biḥamdihi, ‘adada khalqihi, wa riḍā nafsihi, wa zinata ‘arshihi, wa midāda kalimātihi" (Glory be to Allah, and praise be to Him, by the number of His creation, by His pleasure, by the weight of His Throne, and by the extent of His words). And Allah, the Exalted, knows best.