mac mini m4 doesn't work correct with asus thunderbolt 4 DC500

You appear to have misidentified your monitor. The link that you provided is for the Acer XV275U P3, which has a resolution of 2540x1440 pixels. The screenshot indicates that the monitor is an XV275K P3 – and is offering both 3840x2160 and (Retina) 1920x1080 (Default) settings.

Acer – XV275K P3

This appears to be a 27" monitor with a resolution of 3840x2160 pixels; and USB-C, DisplayPort, and HDMI inputs. The USB-C and DisplayPort inputs support refresh rates of 48 – 160 Hz; and the HDMI input supports refresh rates of 144 Hz.

3) Default resolution is 1920 x 1080 but my monitor supports 4k

That's normal. That is almost certainly a Retina mode, in which

• Applications size text and objects "as if" the screen had the Displays Settings ("UI looks like") resolution.
• The Mac draws text and photo areas in detail on a canvas that has twice as many pixels in each direction.
• The Mac scales or copies the contents of the canvas onto the actual 3840x2160 pixel screen.

1920x1080 is probably the "(default)" because it corresponds to a 3840x2160 pixel drawing canvas, a canvas that has exactly the same resolution as your screen.

On a 27" monitor, you may find that Retina "looks like 2560x1440" mode has a better tradeoff between workspace and text size. The scaling isn't as "pixel perfect" as with Retina 1920x1080 mode, but I find it more usable, overall. Note how, when you are using this mode on a 4K monitor, the Mac draws things in 5K detail. This doesn't turn the 4K screen into a 5K one – but it is a way of making "like 2560x1440" mode use all of the 4K screen's resolution.

You need give up the idea of connecting both of those displays thru a hub or dock.

For the best results, you need to connect both of those displays directly to the M4 Mac mini.

see > Connect a display to Mac mini - Apple Support

One or both using a short 3.3' high speed VESA Certified Thunderbolt/USB-C to DisplayPort 1.4 8K cable.

for example > https://www.amazon.com/dp/B0BXLDJV3Y/ref=sspa_dk_detail_5?

Or optionally one using a short 3.3' high speed Certified 2.1 8K HDMI cable from the M4 Mac mini.

for example > https://www.amazon.com/dp/B0CQP27WZ2/ref=sspa_dk_detail_3?

2) I can select refresh rate only between 30 and 600 hertz (my monitors max refresh rate is 144 hertz)

I assume that you meant 60 Herz – not 600 Hertz.

Driving a single 6K (6016 x 3384 pixel) monitor, running at a refresh rate of 60 Hz, requires pushing 1,221,488,640 pixels per second. Driving two UHD 4K (3840 x 2160 pixel) monitors, running at a refresh rate of 144 Hz, requires pushing 2,388,787,200 pixels/second. You want to drive the equivalent of two 6K monitors over a single dock, and I'm skeptical that is going to happen. The usual rule is "one 6K monitor at 60 Hz, or two 4K monitors at 60 Hz."

Then there are the Technical Specifications for the M4 Mac mini

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M4

Simultaneously supports up to three displays:

• Up to three displays: Two displays with up to 6K resolution at 60Hz over Thunderbolt and one display with up to 5K resolution at 60Hz over Thunderbolt or 4K resolution at 60Hz over HDMI
• Up to two displays: One display with up to 5K resolution at 60Hz over Thunderbolt and one display with up to 8K resolution at 60Hz or 4K resolution at 240Hz over Thunderbolt or HDMI

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You might be able to drive both displays at 144 Hz if you connect them to separate ports on the Mac mini, but there is no promise that you can do so. Looks to me like the specification only promises that you can drive one display at 144 Hz, at the cost of reducing the maximum number of displays to two.

"1) MacOS can see only one display and the second works as mirror"

This is probably due to your choice of dock. Macs can drive one monitor over a plain USB-C dock; up to two over a Thunderbolt 3 or 4 dock. Your Asus – ASUS Triple 4K Thunderbolt™ 4 Dock DC500 has three display outputs, and this makes it very likely that it is driving some of them in ways that Macs do not support.

If I had to guess, I would say that this dock is using one of the two video signals from the Mac for its Thunderbolt 4 daisy-chaining port, and the other to drive both of its HDMI 2.1 ports using DisplayPort MST. Macs do not support this. A typical symptom is that the Mac only thinks that one monitor is attached, and that the monitors "mirror" the same image, because, in effect, the dock is "photocopying" a single video signal behind the Mac's back.

If you are plugging both monitors into the dock's HDMI ports, I would suggest changing things so that one monitor is plugged into one of the dock's HDMI ports, and the other is plugged into the Thunderbolt 4 daisy-chaining port.

Servant of Cats wrote:

You appear to have misidentified your monitor. The link that you provided is for the Acer XV275U P3, which has a resolution of 2540x1440 pixels. The screenshot indicates that the monitor is an XV275K P3 – and is offering both 3840x2160 and (Retina) 1920x1080 (Default) settings.

Acer – XV275K P3

This appears to be a 27" monitor with a resolution of 3840x2160 pixels; and USB-C, DisplayPort, and HDMI inputs. The USB-C and DisplayPort inputs support refresh rates of 48 – 160 Hz; and the HDMI input supports refresh rates of 144 Hz.

Good eye, I initially missed the difference in the link and screenshot.