Thanks for your patience, we finally found some time to try this on Win 7.
The latest Arduino states it is for win 8.1 or 10 only, so we downloaded an older version, 1.8.0
We got the full installer as it will also install drivers.
After several times agreeing to install untrusted drivers anyway, the install went well.
Then in the Arduino software, you should select board "Arduino Leonardo" since the Pro Micro is not an official Arduino model. Then plug in your Arduino and select its port.
We did encounter some errors flashing at first. We were connected to a USB3 port on that machine. Looking around on the web, win7 and USB3 have issues with Leonardo. Later we connected to a USB2 port and the code upload worked. I believe it is a known issue with windows 7 and USB-based arduinos that when you reset the Arduino to program it, sometimes win7 will assign a different com port number to it, so the software will not see the Arduino anymore. We were getting that on our USB3 port, but somehow the USB2 port worked ok.
Have a look at this as it might help: