[HTFreak]

Just in case I want to secure the edge of the fan where it meets the roof
as shown in this photo to make it more waterproof, what type of caulking
is best for this application? (all around the entire circle, not just where the arrows are).

 

[3onthetree]

I would leave it alone. If there are water problems that would be above any sealant and the water might just sit there and rot. I'd want to see if there is a leak.