Is it permissible to shorten and combine prayers, and for a traveler to fast, given the time difference in Japan for three months?

It is not permissible to travel to non-Muslim countries except out of necessity, such as seeking beneficial knowledge not available elsewhere, or inviting people to Islam, while adhering to Sharia (definition) guidelines. If the duration of stay is four days or more, the ruling of travel ceases, and prayers are performed in full. As for fasting, it is not affected by time differences as long as night is distinguishable from day, and one must abstain from all things that break the fast from the rise of dawn until sunset.