How to get Baite Pro Mini working?
I have several clone Pro Minis I got from several sources on ebay for ~ £2 ($3) each. I also use Ubuntu (10.04 on this old PC but it's fine).

I started with a USB converter similar to yours and it was a bit hit-and-miss choosing when to press the reset to upload. Once I got connections right and worked out when to press reset it became a more reliable procedure but still a pain. 

I realised that it would be better to use the auto-reset from DTR so I got a cheapo USB to serial from ebay which claimed to be FTDI (or compatible?) though I didn't know what that meant at the time. With a small converter board to make the right connections it works well.

Your connections look good so if you haven't damaged anything it's probably a matter of when to press reset. Windows won't help!

You must choose the correct board in the Tools menu of the Arduino IDE - Pro Mini with correct AVR chip, speed and voltage. I use programmer AVR ISP (I think)