I have a Nook, not a Kobo. Nooks also have problems with covers not showing up for SD card sideloaded books. For the Nook, the fix is to use Calibre to re-convert EPUB to EPUB. Delete the book from the SD card that doesn’t have a cover, then add the re-converted book.
Do you attach the Kobo to your PC with the SD card in it, or do you remove the card and put it directly into the PC’s card-slot? I leave the card in the Nook, and Calibre has no problem recognizing it. I get an icon for the “Device” and an icon for “Card A”. Click the Device icon and you see only the books in internal storage; click “Card A” and you see only the books on the SD card. Do you see both icons when you attach the Kobo to the PC?
SD cards have a “Speed Class” (1,2,4,6,10) with the higher numbers faster. For most eReaders a class-4 is fine; higher speeds are needed for devices like HD-Camcorders. I use a 4-GB capacity Sandisk with a Class-4 speed-rating and it works fine. If the card does not show a number in a semi-circle, it’s probably a golden-oldie speed-1 … IMHO too slow.
Hope some of this Nook stuff can help with your Kobo.