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.
For passing time, my friends and I have called a famous diviner. She told me that somebody had cast a spill on me not to get married for the rest of my life. I didn`t believe her, but I can`t forget her words. How can I protect myself from such thing?
Praise be to Allah the Lord of the Worlds.
Dealing with diviners is forbidden and what you are suffering from is due to your having consulted that diviner. Have trust in Allah and ask Him for forgiveness, but rest assured that whatever Allah has decreed will take place. And Allah The Almighty Knows Best.
Is it permissible to make ablution without answering the call of nature after waking up?
Washing front and back openings (Istinjaa`) is not a condition for the validity of ablution because it is done to remove Najaasah (impurity), thus if there is no Najaasah, there is no need for that, and then it is permissible to make ablution without answering the call of nature. However, prayer is invalidated if there is Najaasah on the anus ,or the front opening, so it (Najaasah) must be removed for the prayer to become valid, and not the ablution.
I made a vow "If the Israeli troops retreated out of Gaza strip I will buy a cake from a certain bakery" and it happened. Am I obliged to buy from the same bakery?
You are obliged to buy from the same bakery. And Allah Knows Best.