What is the ruling on swearing on the Holy Quran and breaking that oath?
It is impermissible to swear on the Holy Quran in vain, and it is also impermissible to subject it to such an act since breaking the oath after swearing on the Quran entails an expiation.
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 missed fasting 30 days of the obligatory fast within the last 6 years and 20 days. How do I fast? And what should I do?
Missed fasting days must be made up, and it is permissible to make them up on non-consecutive days, as continuity is not required for making up missed fasts. Additionally, expiation (Fidya) must be given: feeding one needy person for each day if the makeup is delayed for one year. If the delay extends to two years, Fidya must be given to two needy people per day, and so on. And Allah Knows Best.
Is it permissible for a woman to sit with her brothers-in-law?
It is impermissible for a woman to sit with her brothers-in-law, and it is also impermissible for a person to have a Khulwa (seclusion) with his sister-in-law.