if I reformat the sd card, the data in the card will all be lost including the camera program. will the camera work properly if I insert back the reformatted sd card?
When you format a card ALL data on the card is erased. If there are important files on the card that you want to keep you should copy them to a storage device such as your computer so that you can copy them back onto the newly formatted sd card.
I am not familiar with the Blackvue operation, but if I put a blank SD card in my Finevu the files mandatory for operation are copied from firmware to SD card. Also the directories are created. Does a Blackvue not act in the same way?
Same with my luksa, if i put a complete blank Card in to the camera will copy its config from FW to the SD Card, and create all the destination folders for the footage.