One common theme is mystery-solving. Since they are often involved in mysteries in the original show, fanfictions often continue this trend with them working together to solve a new mystery in their town.
Sure, they are. They play important roles and their relationships and adventures are part of the comic's established canon. There are many story arcs featuring them both.
Betty and Jughead's relationship in the comics is complex. Sometimes they are together, but there are also times when they face challenges or are not in a romantic connection. It all depends on the plot and character development within each comic issue.
You can try some popular fanfiction websites like Archive of Our Own (AO3). It has a large collection of Betty x Jughead fanfictions. Just use the search function on the site and type in 'Betty x Jughead' to find relevant stories.
Jughead and Betty did have a dating phase in the comics. It was a significant part of their character development and added depth to the overall story.