1) What scholarships exists in my area?
At this phase of your education, you should be talking to your advisers on a regular basis, or at least reading all of the material they send out. Usually advisers will send out all kinds of scholarship information as they receive them. So, your best bet is to talk to your adviser. You can also try scholarship search engines, many scholarships are not location-dependent.
2) What Universities have open post-doc positions? Beside Princeton/IAS I did not found organized information in other universities.
This one is tricky and I recommend talking to your adviser here also. Many opportunities aren't advertised openly - it isn't always what you know, but who you know. Also consider that there may be opportunities and projects in different departments other than CS that need services a CS student can provide.
If you've already looked but couldn't find anything, then contact the advisers at those schools.
3) How can I chose the right people to ask recommendation letters from?
Think about all of the people in the institution you have worked with. Advisers, teachers, mentors, ... Now, you want to choose the best people based on :
- Choose those who knew you and worked close to you
- How high ranked are they, how much relation do they have to your desired postdoc position?
- How well do they think of you? Did you do good work for them? Did you get high grades in the class? Were they "wow!"ed by your performance?
4) Assume that someone wants that I will come to his university to do a post-doc and this will require some effort to hire me(need to find money ...), but my first preference is other university which I still do not know if will want to hire me. What should I do in this case.
It's up to you. I think it's better to be open to everyone that you haven't decided yet so they are more understanding if you take a different route. When an offer does come up, just like a job, I think you can wait about a week before deciding. After that, you are stretching your luck.
Just remember that you don't want to burn any bridges here, be patient and open, and a solid offer has much more weight than a "maybe".
