Re-taking the test?

Hi, quick questions:

As I have doubts that I will get high enough score for TOEFL iBT, which I took on May 4th (I’ll learn the results on May 23rd), I would like to know when exactly can I register to take the test again?

How much time should pass after the day, when I first time took the test?

Will my score for the test (second time taken) be valid?

TOEFL listening discussions: A conversation between a professor and a departmental secretary