Hi!
"1) Are there any other (easy) methods to reach the relaxed learning state?"
You mean besides the 3-2-1 method suggested by Paul Scheele? Oh yes. But they're about the same, really. There's Silva, a few breathing techniques and others which are less relevant to learning, which include things like sophrology. Of course, some mind machines do that as well, though I am personally not entirely happy to let one put me into the accelerative learning state when I can do it (and faster) myself. With practice, you'll be able to enter the state with a breath.
"2) A friend of my told my about a brainmachine, but what does this machine do?"
As you have probably discovered from the Tools for Wellness site, there are a good many mind machines which accomplish different things. An outline (though maybe slightly outdated) of what they do can be found in Superlearning 2000. I am not qualified to comment further as I have not personally used these machines.
"3) I have also heard that one can study at high level when he is in the alfha state. Do we have to be in this state for PR?"
The short answer would be yes. You might even call the accelerative learning state the alpha level if you like. This is when the other than conscious mind is dominant, and you are most receptive to information.
KWLee