Questions about OKdo Raspberry Pi 4 Power-HAT Case

Even the manufacturer does not list on the product page which fans would be compatible: https://www.okdo.com/p/okdo-raspberry-pi-4-case-with-power-button-black/#product-details

Yes, all you have to do is install the Pi in the housing, plug in the board supplied and configure it using the commands in the manual. Basically easy, but there is no fan included and unfortunately I haven't found a suitable one.

No. The Raspberry Pi also runs without cooling. However, it can also be overclocked and cooling would then be necessary.

Dimensions: 1.2 x 1.2 x 0.3 (inches) In cm: 3.048 x 3.048 x 0.762

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ok, is to be understood completely different, a huge circuit board for switching on and off...