Does passing wind, from the anus without a smell, invalidate prayer?
If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.
When is a child instructed to fast?
A child is instructed to fast at the age of seven if they are capable of fasting and have reached the age of discernment, by analogy to prayer. They should be encouraged but not forced, so they can become accustomed to it. It is obligatory for their guardian, whether a father or another, to instruct them.
Should missed Sunnah prayer be made up?
Making up missed voluntary acts of worship is from Sunnah.
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.