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.
It is stated in the Noble Quran that pork is forbidden for Muslims. Why is that so?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
To Allah belongs the dominion of the heavens and the earth and He makes certain things allowed for us, while others are declared prohibited. Consequently, He the Almighty wouldn`t make something prohibited unless it is harmful; whether we are made acquainted with the reason or not. Moreover, medical doctors have stated that there are many harms for pork. And Allah The Almighty Knows Best.
What is the ruling on buying a car from someone for less than the market price, because they are in a hurry to travel and want to sell their belongings at a lower price due to their urgency?
Yes it is permissible; however, a Muslim shouldn't take advantage of other's difficult situations.
What is the ruling on Qonot Du`a (supplication) at dawn prayer?
All perfect praise be to Allah, The Lord of The Worlds
It is a confirmed Sunnah, and whoever leaves it should perform Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.