Hi, this adapter is for Canon EOS mount lens to Sony E NEX mount camera, we checked the sony a 7iii camera mount is E mount , this adapter can fit it , but you can reconfirme it , thanks.  

Yes, it will fit any Sony e mount body, either full frame (a7..., a9...), or aps-c (like a6500, etc) 

There are 6PCS adapter ring included in this flash, here is the size:
52 55 58 62 67 77mm, as long as your lens size is one of them, then could be used,
Here is the way to check your lens size:
Your camera's lens thread size will be marked somewhere on the lens barrel or printed underneath your lens cap. This number is always preceded by a "?" (diameter) symbol. For example: ?52 = 52mm lens thread size.
If your lens size is none of them, please tell us, we may include the size you need but at this case, this item must be shipped from China so that we could pack with this adapter ring you need. 

Yes the FD-NEX adapter is what you need. I also have a a6000 and a Canon FD 50mm , 28mm, and a 300mm and they all work well with this adapter. 

Yes. NEX-5T is a APS-C crop sensor. I've used these sensor cleaners on my Sony A6000. They work very well.