Is it permissible to offer mandatory prayer while sitting?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.
What is the ruling on a second congregation [being formed] in the mosque?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is disliked to deliberately seek to establish a second congregation in a mosque that is not one frequented by transient passersby — such as a neighborhood mosque with a regular, appointed imam — unless permission is granted by that imam, since doing so implies criticism and an affront to him. However, if the mosque is one frequented by transient passersby — such as mosques located in marketplaces — then a second or even third congregation is permissible there, whether or not it has a regular, appointed imam, and whether or not that imam gives his permission. This is because such mosques experience a continuous flow of people coming and going, so no implication of criticism toward the imam is perceived in the formation of multiple congregations in that setting. And Allah, the Exalted, knows best.
What is the ruling on performing the standing (qiyām) and bowing (rukū‘) portions of the prayer normally, while performing the prostration (sujūd) seated due to knee pain?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If performing sujūd (prostration) in prayer causes the worshipper pain in the knees, then it is permissible for him to perform it through gesture (īmā') while seated, since Allah, Glorified and Exalted is He, has lifted hardship from His servants. On the authority of ‘Imrān ibn Ḥuṣayn (raḍiyallāhu ‘anh), he said: "I suffered from hemorrhoids, so I asked the Prophet ﷺ about [how to perform] the prayer, and he said: 'Pray standing; if you are unable, then sitting; and if you are unable, then on your side.'" [Ṣaḥīḥ al-Bukhārī]
If the valid excuse later subsides, the worshipper is then obligated to perform the prayer with all its pillars and conditions fully observed — including standing, rukū‘ (bowing), and sujūd (prostration). And Allah, the Exalted, knows best.
What is the ruling of Islamic Law on applying perfume before entering the state of ihram
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Applying some perfume (ṭīb) before entering the state of iḥrām does not affect the validity of the Ihram, even if its trace remains after the iḥrām has begun. Indeed, it is sunnah for the pilgrim performing Ḥajj or ʿUmrah to perfume himself before iḥrām.
The scholar Nawawī al-Jāwī (may Allah have mercy on him) said: “The third of them is applying perfume to the body shortly before it, that is, before iḥrām, whether the one entering iḥrām is male or otherwise, young or old, married or unmarried. The recommendation applies after performing the ritual bath (ghusl), and it is fulfilled with any perfume whatsoever, though the best is musk, mixed with rose water or the like. There is no objection to the perfume remaining on the body after iḥrām; however, if a woman becomes bound by the mourning observance (iḥdād) after entering iḥrām, she must remove it. As for perfuming the garment, it is merely permissible, not recommended, according to the reliable position (al-muʿtamad). But if one removes his perfumed garment while the scent is still present in it and then wears it again, he is liable for the fidyah (expiation).” [Nihāyat al-Zayn, Vol.1/212]. And Allah Almighty knows best.