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 for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.
Should missed Sunnah prayer be made up?
Making up missed voluntary acts of worship is from Sunnah.
Can an Udhiyah be made up if its time is missed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the sacrificial animal (udhiyah) is a voluntary (nafl) offering and its prescribed time is missed after the three days of Tashriq have ended, then it is not to be made up as a sacrifice; rather, it becomes merely a sheep for meat.
However, if it was a vowed (nadhr) sacrifice and its time is missed, then it must still be slaughtered, and the slaughtered animal is to be treated as it would have been during its prescribed lawful time. And Allah Almighty knows best.