Should be FAT32
otherwise with exFAT you're just going to end up with a corrupt sdcard. U should not be trying format it on the pc anyway.
When u did chkdsk make sure you choose repair boot also, then format the card in a smart phone. I think your card is legit and not a fake, it somehow got corrupt, but is fix'able. This happend to me after a bad ROM FLASH, but was easily repaired with repair boot from chkdsk cmd.
Unrooted Xoom WiFi running Android 4.1.2. I did as you laid out: PC chkdsk (found and repaired boot corruption), formatted in my Galaxy S3 (unrooted running Android 4.3, verified amount of free space shown available), turned off Xoom and entered card, booted Xoom. Storage says to Mount SD Card, meaning it knows something is in the slot, but card will not mount. Have gotten smaller cards to work in Xoom.
Does anyone know what else I might try?