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.
Which is better for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.
Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.
Which is better in night prayer: long standing (Qiyam) or long prostration (Sujood)?
Long standing (Qiyam) is better in prayer. However, a Muslim should also observe tranquility and composure in their prayer.