Is it permissible for the mother to give her children from the Zakah (obligatory charity) of her money?
It is permissible for the mother to give her children from the Zakah of her money if they are Zakah-eligible recipients, and she isn`t obliged to provide for them.
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.
Is it permissible for a Muslim to slaughter an Aqeeqah on behalf of someone else, and offer it to him as a gift?
In principle, the guardian is the one who should offer the Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth) because he is obliged to provide for the newborn, and it is impermissible for anyone else to slaughter it on his behalf unless with his consent. However, it is permissible for a person to offer the sheep, or its price as a gift to the guardian of the newborn, and then the latter can slaughter it, or deputies someone else to do that on his behalf.
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.