HDMI TO USB ADAPTER

what are you trying to accomplish by that?

only thunderbolt (where the 3g and 4g use usb-c) carry any form of direct video signals

for normal usb to deal with visuals a usb graphic card or a tvtuner with hdmi in would be required

No HDMI does not convert to USB-A.

If it is a new Mac Mini, then you can not use an iMac as a display. Likewise only certain iMac models can be used as a display for another Mac. see > https://support.apple.com/en-us/HT204592