Check-in and Check-out

Hello dear forum users!
I have a question about Check-ins and Check-outs in Hotels in Japan and I would love your help.

In our trip to Japan (April) we will be staying in numerous hotels across Japan.
In many days, we will arrive to our hotels before check-in time.
1) Our question is this: Is it OK to arrive to the city and hotel before check-in times, getting to the reception and asking them to keep our luggage and suitcases with them, while we travel around the city until we come back in check-in time? Is it safe (for the luggage)? Is it customary to do that?

Another question is about the check-outs. In many days in our trip we will be planning to stay at a hotel/city for a few days, and after the night leave really early in the morning to the next city (5am-7am).
2) Is it a problem in Japan? We don't want to waste too much time so in many cities we would like to leave the hotel very early, is there something special we need to do for that?

Thank you very much!

1) no problem at all. many Japanese are doing like that.

2)early departure: it depends on the hotels.
if I were you, I pay all the money at the last night and do not drink room beverages, provided by the hotels, to avoid additional payment.

In ryokan, you may not have a time to eat breakfast.

As @Ken has said. Leaving your luggage before check in is quite normal. As for check out I generally leave a little later 9 to 9:30 ish to allow me to have breakfast at the hotel & to avoid the morning rush hour. Besides I am on holiday & most travel days for me are not more than a few hours so I am still at my destination by lunchtime.

In large Western-style hotels the front desk is open 24 hours, so you can check out whenever you want (but confirm the hours of the front desk with your hotel beforehand).

If the front desk is not open, you may stil be able to check out by depositing your key in a box, ask the hotel.

Yes. Pretty much like anywhere else in the world.

As others has mentioned, you can leave your luggage before check in, as for checkout, whiles making the reservation do inform the hotel in advance, some hotels will kindly ask you to make payment during check in, that's if the hotel normally request payment on check out during leaving.

some hotel or ryokan has breakfast as earliest as 0700, anything before this time, you won't be provided with breakfast, the hotel or ryokan will tell you this during check in.

I use Toyoko Inn hotels and I pay when I check in. I don't know if it's a requirement, but I'd rather do that so I can take advantage of the free nights you get with membership.

With all my bookings during my visit, the ryokan's and hotel's require me to pay in advance, which I think is normal in japan, this year I will be staying at takaragawa onsen for one night and through booking.com, I've told them I will check out around 0400-0500 , they replied if I could pay for the reservation in full during check out, so I assume some ryokan and hotels have guest to pay during check out.

correction to my last post, it should state check in on the last line.