Work in Japan in what sort of job? A bachelor's degree is sufficient for a work visa in many cases (depends on the category of work visa), but employers may want additional qualifications, proof of language skills, experience, etc.
are you a student in Japan?
Then you will apply for jobs at the end of your 3rd year, 1 year before your graduation.
So if you are graduating in April, 2015, you should have submitted your applications in January and February of 2014, interviews in March and April of 2014, and get offer in late April 2014. Then you finish up your last year in university. This is the ONLY window to apply for new grads, so do NOT miss it. If you are graduating 2015, see if there's ANY application that's still open, most have probably already closed, so hurry up. If you are graduating later than 2015, then do what I said next year.
yes, the diploma is the only thing that's required. It is MUCH easier to get hired as a new grad than an experienced hire, opposite of most countries. In fact, having experience will often hurt your chances. Japanese companies hire very few experienced hires. Also your major doesn't matter, most Japanese companies will train you from scratch, so feel free to apply for positions as far as system engineers if you so choose.
For international universities, please go to one of the career forums, such as the Tokyo Summer Forum.
I know Boston Winter Forum is the biggest, but generally unless you are from a top tier university like Harvard, it is too competitive.
you have to land a job before you graduate. The timeline for applications will not change much from the Japanese one. Once you graduated, Japanese companies will be recruiting for the next year's grad, and ONLY next year's grads and you'll have no chance. Find companies that you are interested in, and follow their recruiting websites for new grads closely.