The research student period is mentioned in the
guidelines. If you leave in April, you can stay as a research student for 2 years. If you choose October you can stay as a research student for 1 and a half year.
You can attempt the entrance exam anytime during that period. That depends on when your university has the entrance exam.
Are you going for Master's? Write a research proposal for 2 years then. Dont include the research student period. Thats what I did.
If you are confused about the dates, assume that you will join the course 6 months after you arrive in Japan and add the dates accordingly.
(
2018年度大使館推薦による国費外国人留学生(研究留学生)の募集について:文部科学省 )