How easily can a microcontroller be damaged by mishandling?
It seems that the MCU board doesn´t have a reverse protection with
an diode. So it is possible that you kill the board (other solution
is, that you put +5 V on a GPIO of the MCU). 
I don´t think that
you get a good connection with your fingers, so I think that wasn´t
the issue (maybe ESD?). 
Very unlikely. I disconnect/connect all
devices to my MCU, while the MCU or the device is powered. 
This is
an option with every delivery.