With the three pieces of information, you can always determine one of the other two provided (though, really one piece of information. The power of the test just is 1 - beta). I suggest reading up on the power of a test (an important concept in study designs). Wikipedia is a good place to start.
As for the type of errors, look up what type 1 and type 2 errors mean and the definitions of and . You'll see a profound similarity