Is it permissible for a wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
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.
What is the ruling on speaking while relieving oneself?
It is disliked for one relieving himself to speak while doing so, except out of necessity. And Allah the Almighty knows best.
What is the ruling on Tarawih prayer?
Tarawih prayer is a confirmed Sunnah (Sunnah Mu’akkadah).