That is a CH340G serial adapter; normally you need to install special drivers for that - but it looks like you've done that? Those are the good CH340G serial adapters (among other things, they're what I ship as the optional serial adapter in my Tindie store) - I've yet to encounter a bad one.
First do loopback test with that serial adapter, to confirm whether the serial adapter functions.
Assuming it does, connect the pro mini, press and release reset and watch the led on the pro mini. Does it blink? What kind of blinking pattern (if it's a triple blink, then it's running optiboot not the normal pro mini bootloader, and you should tell the IDE it's an Uno)
When you try to upload, does the light on the board do the same thing as if you pressed reset?
Do you have the DTR line connected?