One common theme is the development of the relationship between Uzaki and the male lead. It often shows how they grow closer over time through their various hang - out sessions.
Another good place could be Fanfiction.net. There are often many talented writers who contribute to this series. However, the quality can vary, so it's a good idea to read the reviews or summaries first. Some fanfics might focus on the comical interactions between Uzaki and the main character, while others could explore different aspects of their relationship in more depth.
Yes, the Uzaki-chan manga has come to an end. The creator completed the story and it's no longer ongoing. Fans have had the chance to see the full tale unfold.