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.
Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
How should a woman make up prayers that she missed two days from delivery?
All perfect praise be to Allah,The Lord of The Worlds It is prohibited to delay prayer beyond its prescribed fixed time, therefore, the woman in question is obliged to make up missed prayers after delivery and confinement i.e. once she becomes ritually pure. 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.