Is continuous, involuntary flatulence, as well as the involuntary emission of bubbles from the vagina, considered nullifiers of ablution? What is the ruling on the prayer of someone to whom this occurs? And does she bear the sin of her brother if he asks her to play music, while she has repented?

If the emission of gas is merely a doubt, then purification is not invalidated. However, if there is certain conviction of its emission, then it is invalidated. Prayer performed while holding back gas is valid. If you are afflicted with incontinence of gas, then perform ablution for each prayer after its time has begun and pray the obligatory and supererogatory prayers. As for your brother and his listening to music, his listening does not harm you as long as you have repented, and you should advise him by explaining the prohibition of listening to musical instruments.