Which is better, to pray at a prayer place (Musala) whereas many people pray in it, or at a near by mosque in which a few people perform prayer?
Praying at the mosque that has a bigger number is better so long as the number of praying people at the other mosque permits performing prayers in congregation. And Allah Knows Best.
Is it permissible for a woman to adorn herself with kohl (eyeliner) and go out wearing it?
Kohl is a form of adornment, and it is forbidden for a woman to display her adornment to anyone other than her husband or a Mahram. And Allah Knows Best.
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.
Is it permissible to repeat the Istikhara (seeking guidance) prayer, and is it a condition that one should sleep after offering it?
All perfect praise be to Allah,The Lord of The Worlds Istikhara is offered once, but it is permissible to repeat it, and sleeping after offering it is not a condition for its validity. And Allah Knows Best.