As to your first question: this will be much easier to accomplish if you carry the laptop with you into Japan. That way, there'll be no question that it's your property, acquired before entering Japan, and that because you're going to be present only temporarily in Japan, no Customs duty should be assessed.
・Source: A page in English from the Japanese customs authority
If the computer arrives separately from you, the box must be specifically labeled so as to "connect" to you, and you must declare the contents when you yourself enter Japan. These requirements are set forth in the Japanese Customs page linked above under "Unaccompanied baggage."
The page linked above says that upon your own entry and declaration about unaccompanied baggage, you receive a "clearance" document which allows importation of this property without duty. It's unclear what happens to such package if it arrives before you do. I also wonder how you could complete the declaration during your own entry if the computer is new, hadn't been in your hands, and presumably you wouldn't have or be able to disclose its serial number.
As to your second question: I have no idea, never having done this.