Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
Is it permissible for a suitor to go out with his fiancé upon the conclusion of the marriage contract?
Upon the conclusion of the marriage contract, the woman becomes lawful for her husband. However, the customary practice should be observed in this regard since rights could be lost in case of divorce, or death.
My husband has deprived me of visiting my family and is threatening to take my 7-month-old baby girl. Is he entitled to do so?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Your question is unclear, but family visitation is a legitimate right of yours. However, if he deprives you from this, try to convince him with wisdom and fair preaching. If there is a problem between you two, try to fix it. As for your daughter, you are most entitled to her custody anyway. Even if he divorced you, the girl remains under your care so long as you don`t get married. And Allah The Almighty Knows Best.
Is the one who doesn`t offer prostration of recitation during Quranic recital considered sinful?
Prostration of Quranic recital is a Sunnah due on whosoever recites a verse that contains a prostration. It is also a Sunnah for the reader and the listener. However, none of them is considered sinful for not offering it, but they deprive themselves from a great reward. It is obligatory to offer the prostration of Quranic recital in congregational prayer following the lead of the Imam.