Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
I`m in love with a certain man, and want to marry him in particular, but my family refused that, what should I do?
The father should know what is in the best interest of his daughter and consider her situation. On her part, the daughter should trust her father`s view point as far as suitors are concerned. Moreover, it is prohibited for any woman, or girl to get involved in a relation with a non-Mahram (Marriageable man).
Where should a woman who is led by her husband in prayer stand?
All perfect praise be to Allah The Lord of The Worlds It is from Sunnah (Prophetic tradition) that she stands behind him. And Allah Knows Best.