Does Laylat al-Qadr move between the nights of Ramadan?
Laylat al-Qadr is definitely in Ramadan, and it is most likely in the last ten nights, especially on the odd-numbered nights.
For this reason, the Prophet ﷺ commanded observing worship in the last ten nights, and he himself used to dedicate those nights to worship. Many people put special effort into the 27th night of Ramadan, and they are rewarded in any case, whether they actually coincide with Laylat al-Qadr or not, because worshiping on any night of Ramadan carries great rewards.
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.
Is it permissible for a sick person to pray while sitting on a chair?
All perfect praise be to Allah, The Lord of the Worlds It is permissible for a sick person, who is unable to stand up, to offer prayer while sitting on a chair. If he/she was unable to prostrate while on the chair, the he/she should pray while sitting on the ground, but if he/she was neither able to bow (Roku),nor to prostrate, then he can do them while sitting on the chair. And Allah Knows Best.
What is the ruling on the Friday bath (ghusl al-Jumu'ah)?
The Friday bath is a confirmed Sunnah, based on the Prophet's (peace be upon him) saying: "Whoever performs ablution on Friday, it is good for him, and whoever takes a bath, bathing is better." (Reported by Abu Dawud and al-Tirmidhi who said it is a hasan hadith). It is recommended for everyone who wants to attend the Friday prayer, even if they are not from its usual attendees, like a woman or a boy.
If a person is in a state of major impurity (junub) and intends by his bath both lifting the major impurity and the Friday bath, he achieves both. If he intends only one of them, he achieves only what he intended. And Allah the Almighty knows best.