Does wiping over one's socks during ablution permissible?
If the socks were thick, then wiping over them during ablution is permissible so long as wiping conditions are observed. And Allah Knows Best.
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 the man to go out wearing shorts?
All Perfect Praise is due to Allah, The Lord of The Worlds
It is permissible so long as his Awrah (private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed. And Allah Knows Best
What is the ruling on having slight discharges of menstrual blood during daytime of Ramadan, and before Maghrib time?
A woman who is certain that her menses have started during daytime of Ramadan is in a state of menstruation, and her fasting is considered broken at first sight of blood. However, she is rewarded for not breaking fast at the beginning of daytime.