Is it permissible to shorten the eyebrows if they get too long?
Yes, it is permissible, but not desirable.
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.
Is love allowed or forbidden in Islam?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
If love refers to the involuntary inclination of the heart, a person isn`t held accountable for it; however, whatever follows this in terms of gazing, meeting, and the like is forbidden. And Allah The Almighty Knows Best.
What is the ruling on determining the sex of the baby whether through killing the female spermatozoa, or any other way in order to have a male?
If it is done through having a certain type of food, taking a certain type of medication, or organizing the time of the marital relation, then it is permissible.