Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
What is the ruling on sacrificing a hornless sheep?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is valid to sacrifice a hornless sheep (al-Jamma’ or al-Jalha’). Similarly, a sheep with a broken horn is also acceptable; it does not affect the validity of the sacrifice even if the break causes bleeding, unless the injury is so severe that it leads to the spoilage of the meat. And Allah the Almighty knows best.
Is it permissible to participate in an Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Regarding the sacrificial offering (Udhiyah), if it is a sheep or a goat, it only avails for one person. However, if it is a cow or a camel, it avails for seven people. It is permissible for the seven participants to have different intentions; for example, some may intend the sacrifice (Udhiyah), some the ’Aqiqah (sacrifice for a newborn), and others may simply intend to obtain meat.
It is stated in Hashiyat Qalyubi ‘ala Sharh al-Mahalli (Vol.4/P.256) and in Bushra al-Karim (p. 706):
"If one slaughters a camel or a cow on behalf of seven... it is permissible. Likewise, it is permissible if some of them intend their seventh for meat, and others intend their seventh for ’Aqiqah." And Allah the Almighty knows best.
What advice do you have for those who spend their nights and days of Ramadan watching TV?
Time is too precious to be wasted on entertainment, let alone in the blessed month of Ramadan, where a Muslim should strive for reward and forgiveness.