Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.
What is the ruling on Tarawih prayer?
Tarawih prayer is a confirmed Sunnah (Sunnah Mu’akkadah).
Can someone who begins a voluntary fast break it?
It is preferable for someone who begins an act of worship not to break it.
Allah the Exalted has said {what means}: "and let not your [good] deeds come to nought!" [Muhammad/33].
However, if a person starts a voluntary fast (nafl) and needs to break it, they are going against what is preferable, but there is no sin upon them.
What is the ruling on eating or drinking during the first Adhan?
It is permissible to eat and drink during the first Adhan because it takes place before the break of dawn. The purpose of this Adhan is to notify Muslims of the approaching dawn so they can prepare to stop eating when they hear the second Adhan.