Oh speaking of the ol' time, MEXT even paid for your medical expenses.
Back to your questions, the answer is no, MEXT won't pay for your travel/conference expenses. When you go to a conference, your lab would pay for it - but it's not like you can go to whatever you want. The school also has funding for that, and typically the lab secretary would take care of the paperwork. But everything has to go through your professor, so ask him directly.