Visitors who stay within 90 days cannot have a bank account. Also, even you have visa to stay more than 90 days, if you stay in Japan less than 6 months, you still cannot have it (you have to stay more than 6 months).
You better visit banks near your house or office. If you visit a bank far from your residence, they will question you.
It depends on the bank. But basically, you need to prepare the following:
1)Public ID with photo ( Zairyu card, passport, driver license, special permanent resident certificate )
If you don’t have any ID above, you need bring the billing statements of water, gas or electricity under your name to prove your present address.
2) Inkan ( Hanko/ private stamp )
Some banks allow to use signature but most of banks require Hanko. In Japan, people use Hanko instead of signature. If you stay in Japan for long, you better have one. Visit Hanko shop near you or you can order on the web.
You can use your cellphone number. If you have a land line, you better use it.
You can exchange in a bank.
But if you want better rate, you should check the reports or blogs of foreigners like below: