As far as I know full sized images are stored in either the mSD card or the drone's internal memory, I think the mSD card is the default. The 'images' on the phone are lower resolution, for me they seem to be about 1/3 or less of the size of the corresponding image on the mSD card.
Personally I find removing the card and putting it into a reader attached to my computer to be the easiest method of transfer. The cable connection does seem slightly faster, 20+ Mb/s vs 18Mb/s for me, but my computer is 'old'.
That said I am biased, I DISLIKE making and breaking micro USB connections any more than absolutely necessary. That said I generally try to leave a card in the 'camera' until it is nearly full before transfering images, memory card prices are cheap enough to carry 32G or 64G 'spares'
I have no recollection of the Mini asking me to format the card when it is refitted but, if relevant, I remove it and refit it with the drone switched off and only very occasionally switch the drone on with out the card being refitted, if I have done so I see a message about switching the storage to the mSD.