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 husband's stand should be, if his wife disagrees with his mother?
Both the mother and the wife have rights on you (Questioner); therefore, you are obliged to treat both justly, resort to wisdom to please both and intiate reestablishing cordial relations among them. And Allah Knows Best.
Should nail polish be removed before making ablution?
Yes, it should be removed because it prevents water from reaching the nails.
Are minors obliged to fast?
A male under the age of puberty isn`t required to fast, but his guardian should order him to fast if he was able to endure the hardship until being used for fasting in general. And Allah Knows Best.