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.
Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?
The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.
Is it permissible for me to name my first son “Kassim” ?
The Prophet (PBUH) prohibited combining his name and his nickname, but using one of them is desirable.
Is it permissible for a woman whose menses exceeded (15) days to pray, fast and do what was prohibited on her to do during the latter period?
If the menses exceeded 15 days then it is deemed menstruation, and in this case she is obliged to pray and fast and to do what was impermissible for her to do during the latter period. In addition, she is obliged to make an ablution for each obligatory prayer after it's due time and making sure that impuity is removed. Finally, your menstruation period is over (Questioner) simlar to your menstruation in the previos month.
