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.

Listening to music is haram, whether in Ramadan or at other times, but it is more forbidden in Ramadan, and is a greater sin. For more, please see the detailed answer.