sterretje:
disconnect the mini, short rx and tx on the adapter, open serial monitor and send some text; it should be echoed back to the serial monitor.
I did do this and rather to my surprise it worked.
I also checked and made sure that the driver version 3.3.2.105 that works with the dubious cloned PL-2303HXs was in fact installed.
I rechecked again that on this device TX and RX go to TX and RX rather than reversed, as is usual, but in neither configuration does anything change. The Mini has power and blink, but never installs nor will it upload the "Blink" sketch.
There is some rigmarole about holding down the reset button on a Mini when starting an upload of a sketch, and I tried all that to no effect, but it seems unlikely to make any difference when the arduino.inf file was never uploaded and the device itself was never installed in Win7 -- as far as I know.
To be sure, where in Device Manager would one find an Arduino device listed?
Thanks!