The answers to your questions:

1. Yes

2. Yes, even tiny bare-bones business hotels do this all the time. It's a simple matter of filling out a form, and any desk clerk can do this. If you have the name and address of your next hotel in Japanese (print it out from the hotel's web page) you will make the desk clerk's job easier. The charge will be about ¥2000, collectable when you make the arrangements.

3. This should be OK, given that you are leaving early in on the morning of Day 1 and not checking into your next hotel until the evening of Day 2. If, for some reason, this arrangement is not possible, the desk clerk will be able to tell you. If it's not, you may have to wait till Monday at the latest.