Is it valid to perform Tarawih prayer at home?
It is Sunnah for a Muslim to perform Tarawih prayer in congregation at the mosque.
However, if a person sometimes prays it at home in congregation with their family for a valid reason, there is no harm in doing so.
Is it permissible to use unscented petroleum jelly (Vaseline) during ‘Umrah, in order to prevent skin chafing or irritation?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
According to the Shāfi‘ī school, it is permissible for someone in the state of iḥrām to use oils and creams free of perfume/fragrance on parts of the body other than the head and beard, for a genuine medical need — such as preventing skin chafing or irritation. However, applying them to the head or beard remains unlawful.
Shaykh al-Islām, Imam an-Nawawī (raḥimahullāh), says in al-Majmū‘ (Vol.7/P.279): "Oils are of two types: the first is an oil that is neither perfumed itself nor contains any perfume — such as olive oil, sesame oil, ghee, butter, walnut oil, almond oil, and similar oils. The use of this type is not unlawful anywhere on the body, except on the head and beard — where its use is unlawful without any disagreement [among the scholars]." And Allah, the Exalted, knows best.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
What is the ruling on omitting the prostration of recitation?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The prostration of recitation (Sajdat al-Tilawah) is a Sunnah for both the reader and the listener. There is no sin in omitting it, though doing so results in missing a great reward. Muslim narrated from Abu Hurairah (may Allah be pleased with him) that the Prophet ﷺ said: 'When the son of Adam recites a verse of prostration and prostrates, Shaytan withdraws weeping, saying: "Woe to him! (and in the narration of Abu Kuraib: "Woe to me!") The son of Adam was commanded to prostrate and he prostrated, so Paradise is his; and I was commanded to prostrate and I refused, so the Fire is mine."'
Sheikh al-Islam Imam al-Nawawi (may Allah have mercy on him) stated: 'It is recommended to prostrate immediately after reciting or hearing a verse of prostration. If one delays it but the interval is short, he may still prostrate. However, if the interval is long, the opportunity is missed.' [Rawdat al-Talibin Vol.1/P.323].
Furthermore, the prostration of recitation becomes obligatory (Wajib) in congregational prayer if the Imam prostrates, out of the necessity of following him. And Allah the Exalted knows best.