can Mac mini connect to old iMac display?

The very restrictive hardware and OS requirements for the now-deprecated Target Display Mode (TDM) are in this Apple article:

Use your iMac as a display with target display mode

No Mac mini released after 2019 can use any iMac as a monitor.

No Mac mini running Big Sur or newer can use an older iMac as a monitor.

Apple has abandoned Target Display mode in both hardware and software.

You will need to buy a proper monitor for your Mac mini.

No, unfortunately.