Are all the children of a suckling woman considered brothers to the strange child whom their mother had breastfed, or just to the one who had suckled with him?
All the children of the woman who had suckled a strange child are considered his/her brothers and sisters.
Is it permissible to offer Tahajjud prayer after Witr prayer?
It is permissible to offer voluntary prayer after Witr (An odd number prayer performed between Isha and Fajr) prayer. However, it is desirable that the night prayer be ended with Witr. Therefore, it is desirable for one, who thought that he was most probably going to wake up at night in order to offer Tahajjud, to offer Witr after it, but one, who fears that he might not wake up, should offer Witr before going to bed.
Is the marriage, which lacks a valid legal contract, a guardian, and a court registration, valid?
It is incumbent that a valid marriage contract be concluded in the presence of a guardian and two trustful witnesses, and it should be registered in the court to protect the rights of the wife. Actually, a valid marriage contract is what differentiates between sound marriage and fornication.
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.