1. The brownish discharge that comes after the period and after doing ghusl does not matter and is not regarded as menstruation. So your fast is still valid and you do not have to do ghusl after it comes out. 2. The brownish discharge does invalidate wudu. So if you did wudu for Fajr prayer after this came out, then your prayer is valid and you do not have to do anything. 3. If the brownish discharge came out after you did wudu and you did not repeat wudu, then you have to repeat that prayer because you prayed without wudu.

Any bleeding that resumes after the period is over is not menstrual blood. So you can pray, fast, do tawaf or any other acts of worship.

Intercourse at night in Ramadan is permissible. Night lasts from when the sun first sets until (true) dawn comes. It is haram to have intercourse with your wife during the day in Ramadan and it is one of the things that invalidates the fast.

Each woman should act according to her own cycle. If a woman’s period normally lasts for seven days, and she becomes pure before that, then she should pray and fast, according to the more correct of the two scholarly opinions.

Burping does not break the fast, but if some food comes out with it, then it must be spat out. If it is swallowed deliberately, then this breaks the fast.