how do I use a 27" cinema display with a M1 Mini?

If it's the Apple 27" Thunderbolt display, you need a Thunderbolt 3 adapter.

https://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter

If it's the Apple 27" Mini DisplayPort display, you need a USB-C to Mini DisplayPort adapter, such as:

https://www.uptab.com/usb-c-to-mini-displayport-adapter-4k-60hz-silver/

Don't forget to plug the display's USB cable into the Mac mini.

Not possible, unfortunately.

Sorry, misunderstood for target display.