Mac Mini M1 Support 2K 144Hz ?

What external display do you have?

(brand, model, connections)

see "Video Support" at > Mac mini - Technical Specifications - Apple

(HDMI supports up to 4K at 60Hz)

If you external display supports DisplayPort input, then more resolution and refresh rate options are available using a USB-C to DisplayPort 1.4 cable. for examples > https://www.amazon.com/s?k=usb-c+to+display+port+cable

also see > Connect a display to Mac mini - Apple Support

I can not guaranty 144 or 165z, because I do not have that same display.

I can only say that, USB-C to DisplayPort offers a much wider range of Resolutions and Refresh Rates for gaming and wide screen displays than HDMI can.