Square Sail Gaskets- how to loose and tie them

I can't speak to historical methods. This is what I've been taught and found practical in my time.
Ideally, you want to reduce those crinkles on the top of the sail because they can hold water. More important historically when you had organic sails that could rot with the waters help. Not it's more about aesthetics I believe. Flatten them out when you furl it.
You don't want to capture any lines because then it won't set properly, or something else might not work. Every line on the ship should be able to run free.
That black loop is a becket attached to the metal jackstay on the yard that the sail is bent (tied) on to. It's another point to clip in to, so when the sail is furled on top of the yard, and therefore on top of that metal jackstay, you can still easily unclip yourself, not try to dig your lanyard out from beneath the sail.
Ideally you have that triangle of space between the sail and yard, where I stuck the gaskets' bitter end through. It'll be a little harder to tie without that, and that triangle's existence depends how well you've furled and put the sail on top of the yard.