Is it permissible to offer one Rak`ah in Witr prayer?
The minimum of Witr (An odd number prayer performed between Isha`a and Fajr) prayer is one Rak`ah, and the maximum is eleven, but the minimum of its complete form is three, and it is permissible to offer one only.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
Which is better, to pray at a prayer place (Musala) whereas many people pray in it, or at a near by mosque in which a few people perform prayer?
Praying at the mosque that has a bigger number is better so long as the number of praying people at the other mosque permits performing prayers in congregation. And Allah Knows Best.
Is a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?
It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.