Hello and great question!
Printing from your local machine is not recorded and will not impact your bill. If the file sitting on your computer when you are not connected to the internet then you are good to go. The same goes for sharing files and pictures between local computers.
However, printing documents from an online resource will count against you. Anything that needs to be downloaded from the internet (temporary or permanent) will be charged and reflected on your bill. The MiFi only cares about uploads and downloads to the Verizon network, anything else is free.