My Beelink Mini MXIII BOX bricked

Yes, as you could boot the burncard, you can also run CE. The only thing missing to normal release: your box has no bootloader, therefore you need to additionally apply the uboot to the SDcard.

Regarding your repair:
I would not call it an error. Zero device is infinite, so it will write to the partition until it’s full. The strange thing is that the partition seems to have size of 803MB, should be 4MB.
Your partition table seems to be still broken. you should focus on fixing this first (if possible). To fillup the partitions with the right content is quite easy then.
What’s the result of mmc partconf?
Have you tried bumercs tip with modified .ini settings?
Try store init 4 may also work