One common theme is his sense of humor. A lot of fanfictions play up his funny side, like his pranks and witty comebacks. Another theme is his relationships, especially with Amy. Many fanfictions explore their relationship further, whether it's their early days or dealing with relationship problems. And of course, his detective work is also a big theme, with stories about him solving unique cases.
Sure. One great Jake Peralta fanfiction is 'Jake's Big Adventure' which shows him on an off - the - wall undercover mission that's really hilarious. Another one is 'Jake and the Case of the Missing Donut' where his love for donuts gets him into a really comical mystery situation. And there's also 'Jake's Day Off' which gives a fun look at what he might do on a day when he's not at work.
I haven't come across any reports stating that Jake Tapper is penning a novel. His focus seems to be on his journalistic endeavors, such as reporting the news, conducting interviews, and providing analysis. However, it's not impossible for him to venture into novel - writing in the future, but for now, there's no indication of it.