One common theme is power dynamics. Light is often portrayed as having a dominant role, given his intelligence and the way he manipulates situations in the original story. Mikami, on the other hand, is shown as being more submissive to Light's will.
One common theme is loyalty. Mikami's unwavering loyalty to Light is often explored in different ways, like how far he would go to protect Light's plans. Another theme is power dynamics. Since Light has a certain hold over Mikami, fanfictions often play with this aspect.
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.
Another place to look could be FanFiction.net. However, the content there might be a bit more spread out. You'll need to use the search function and specifically look for works related to Light and Mikami in the yaoi genre. Keep in mind that the quality can vary greatly from one story to another.
One popular 'Light x Mikami' fanfiction is 'The Unseen Bond'. It delves into their complex relationship and how they might interact in different scenarios not shown in the original work. It's really interesting to see the author's take on their dynamic.
Since I'm not familiar with this 'yua mikami love story', it's hard to say what the plot is. Maybe it's about a love journey between Yua Mikami and someone else, but without more information, it's just speculation.
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.