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.
I don't have enough information to say exactly who Cap'n Kathy is. She could be an original character created by the fan fiction writer. Maybe she's a pirate - the 'cap'n' part could suggest that - who has some connection to the wizarding world of Harry Potter.
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.