One common theme could be the exploration of their relationship dynamics. It might involve how they interact, whether it's in a friendly way or with some underlying tension.
I'm not sure about specific 'once ler x greed ler fanfic' off the top of my head. You could try searching on popular fanfic websites like Archive of Our Own. They usually have a wide variety of fanfictions in different categories.
I'm not sure specifically what 'Cap deage' means. It could be a very specific term, a misspelling, or something relatively unknown. It might be a proper name, a local term in a certain area or a very niche concept.
The cap man and monkey story is an interesting one. There was this cap man who was traveling around selling his caps. He reached a place near a forest and decided to take a rest under a tree. While he was sleeping, the monkeys in the tree noticed the caps. They climbed down, grabbed the caps, and went back up the tree. When the man woke up, he was confused at first, then saw the monkeys with his caps. He was worried as those caps were his livelihood. But then he remembered that monkeys often mimic human actions. So he took off his own cap and tossed it. The monkeys, being the imitators they are, did the same with the caps they had taken, and the cap man got his caps back.
I don't have the precise release date of Jinx as a manhwa at hand. You might want to check reliable manga or manhwa databases for accurate information.