1) When does 12th grade end in Japan?We don't call it "12th grade", but the last day for students in the final year of senior high school is graduation day which is typically around March 17th or 18th or something like that. Meanwhile, for students in other grades attend school until March 23rd or 24th or so.
2) When are University entrance exams held? (I heard somewhere that it's in January or march...not sure)Here is one typical example of an exam schedule:
http://www.asia-u.ac.jp/admissions/schedule/The earliest entrance exam for the past year was held in Oct 18th, 2016. The type of this exam is called AO exam which puts its emphasis on interviews, and applicants who passed the Oct 18th exam is to take a second exam in mid Nov.
Then there are various types of commendation exams held during Oct 18 to Feb 6, depending on what the applicant is commended by. An applicant would take only one exam of this type.
The traditional type of exams are held during Jan 16 to Feb 25, in which an applicant take only one exam.
There are also other exams held in Oct-Nov for those with special qualifications, such as foreign applicants.
All these are just for one university called Asia University. Other universities have similar systems. Applicants are free to challenge to as many exams per universities as (s)he wants to, as long as the qualifications are granted. But you need to pay about 30000 yen per exam. It's also typical for high school students to take exams for more than one university.
It's typical for high school students to take these exams before graduating so that they can move on to university right after graduation. Otherwise, they need to wait for another whole year for their next chance. In other words, they will be taking entrance exams when they still don't know if they can graduate. High schools will issue a paper that shows the student is "likely to graduate" so that they can apply for university entrance exams.
3) When does the university start?For example, I remember the news reporting that many universities held entrance ceremonies on April 2nd for this year.
Typically, entrance exam results are announced a few weeks after the each exam. Then students soon officially apply entrance and pay a bulk amount of school fee. Again, high school students have not yet graduated at this point. Then they graduate, and then typically around the end of March, universities invite their new students for orientation. And then they are handed their student IDs in April. For the first week or so of April, most of what they do is orientation-related things. Class finally starts after that.
and also...
the first day at school is hardly the 1st of April. - Does this mean that it can start 1 week earlier? or 1 week later?I was talking about high school, but my understanding as a local resident is that it doesn't start earlier, but usually starts later.
Is it because of entrance ceremonies or something?Well, entrance ceremonies are school days. Actually, it doesn't mean much to start right on spot on the 1st when kids still might want to enjoy their spring vacation. And I guess teachers want more time to prepare too.