One great 'Spiderman and MJ Fanfiction' is 'A Day in the Life'. It beautifully captures the relationship between them, showing MJ's understanding of Peter's double life. The story has a lot of heartwarming moments.
Fanfiction about Peter and MJ in the context of Spiderman and Spiderwoman often plays with different timelines and universes. For instance, there could be a fanfic set in an alternate universe where MJ has superpowers too. This would change the dynamics of their relationship completely. Writers can also explore how Peter and MJ interact with Spiderwoman in these fictional stories.
In the traditional Spiderman comic arcs, MJ remains alive. However, there might be alternate universes or special storylines where her fate differs, but in the core continuity, she survives.
A great place to start is Archive of Our Own (AO3). It has a vast collection of fanfictions, including many about Spiderman and MJ. You can easily search for specific tags or ratings to find what you like.
A common theme is also the idea of support. MJ being there for Peter during his superhero battles, and Peter relying on MJ's strength and understanding. And of course, the theme of adventure. Sometimes MJ gets dragged into Peter's adventures as Spiderman, and how they face those together.
One great 'Spiderman x MJ' fanfiction is 'Love in the City That Never Sleeps'. It beautifully portrays their relationship in a modern setting in New York. Another is 'Under the Stars', which focuses on their more private, tender moments.