Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.
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 for a husband to stop his wife from visiting her family?
A husband shouldn`t stop his wife from visiting her family, and it is disliked for him to do so because such an act makes them harbor feelings of hatred against him.
Is it valid to share in the 'aqīqah by contributing a seventh share of a camel or cow?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible. If a group of people jointly share in the slaughter of a camel or a cow on behalf of seven individuals, this is valid — regardless of whether all of them intend the 'aqīqah, or some intend the 'aqīqah, others the uḍḥiyyah, and others simply the purchase of meat. And Allah Almighty knows best.