How to repair FAT table?

[PistolSlap]

I have an external TB data drive. The other day, it wasn't showing up in Computer, so I turned it off for a few seconds and turned it back on. It was detected, but the entire drive was empty. I wasn't told that the drive was unformatted -- it was accessible, just empty.
I did a recovery scan with Recuva and saw that all my files are there. Rather than try to recover them, I am feeling my FAT table is corrupt which is why it is not showing me the files are there. I hear that TestDisk can repair FAT table, and I found this

http://www.cgsecurity.org/wiki/Advanced_FAT_Repair

But I don't understand how to do that from the very beginning when I initiate the program.
Not only that, but the page is talking about boot sectors. Since this is just a data drive with no operating systems or anything bootable on it, I don't think there would be boot sectors? Or am I misunderstanding the term.

I do not have advanced or even basic programming understanding -- my understanding of computers excels within the windows operating system, not code and programming, but I can follow a clear explanation and directions.

Can anyone show me step by step how to use TestDisk to repair this FAT table?
I'd really appreciate it. Thanks

[PistolSlap]

Edit: I went into Advanced and pressed Boot and discovered that any drive needs a boot record -- but upon looking it appears that the backup and main boot records are identical -- See attachment 1. Then I said anyway to rewrite the sector and it said it could not open file system, seems damaged. ??