See pgaskin's
Kobo Firmware Download site and download the 3.19.5761-s firmware which was specific to the Mini. Copy the 1 directory and 2 files from the downloaded .zip file to the .kobo directory on your Mini's SD card. When you re-install the card in your Mini and power on, it should go into the firmware install routine.
For the connection to your computer, have you tried a different USB cable, USB port on your Mac or a different computer? You may also want to try using a USB hub between the MIni and the Mac.
The Mini's factory firmware will not work with current TLS 1.2+ security standards so a WiFi connection will not work. The fix for that is in the last official Mini firmware though I have updated my Mini to the latest firmware with pretty decent results.