Is it incumbent on a family to provide for its old handicapped son and take care of him?
The family and relatives - e.g. brothers - of such a person are obliged to spend on him and take care of him if he didn`t have money of his own.
Is it disliked to clip one`s nails at night, and to burn them afterwards?
It is recommended to bury hair and nails that have been removed and to conceal them in the ground. As for burning nails, we have not found any specific prohibition against it, but adhering to what is supported by evidence—burying the nails—is preferable. And Allah Knows Best.
Is it permissible to listen to chants praising the Prophet if accompanied by musical instruments?
If singing, or chanting in praise of the Prophet was accompanied by a forbidden musical instrument, then it is forbidden.
What is the ruling on performing voluntary prayers during official working hours?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions
There is no harm if there was break time during official working hours, but if not then it is impermissible. And Allah Knows Best.