Overtime rules in Japan (Can I take compensatory leave for the work I do on Saturday?)

Hello, here are the things that I know about my work –

1. We have "minashi zangyo" at my company, where the overtime allowance is already added in my salary, although it is not specified separately in my payslip (only written in my contract).
2. Overtime work on Saturday is added in the "所定休日" column in the system.
3. Overtime work on Sunday is added in the "法定休日" column in the system.

Since last week, the company has opened an outlet shop in my office building. The employees are told to take turns to work on Saturdays when the outlet remains open (0900-1900).

It's been 1.5 years since I am working in this company. During that time, I have worked overtime on the weekend less than 5 times. I don't get paid for the hours registered on Saturdays. I get paid only for the hours registered on Sundays.

My question –
1. Can I take compensatory holidays for the work I will be doing on Saturdays? Is it limited to that month or can I carry it to the next month as well?
2. Is there any way to get paid for the Saturday work? I am more than happy to work on Saturdays if I am getting an equivalent amount. I am reluctant to take a compensatory holiday every time as it might spoil my image.

Please let me know what you think about this situation. Thankyou.