Hiyori remained alive in the Bleach comic. The creators of the comic didn't choose to kill off her character. Instead, she was involved in various plot developments.
Sure, the Noragami manga is completed. It was a great ride with an ending that wrapped up the plot nicely. If you haven't read it yet, it's worth giving a go.
Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own. There, you can search for stories tagged with 'ichigo' and 'hiyori' in the relationship section. Some might be focused on their budding romance, while others could explore how they support each other through different challenges in their fictional world.
Noragami is about a minor god named Yato. He wants to have a grand shrine and a lot of followers. He meets a girl named Hiyori who can partly leave her body due to an accident. They get involved in various supernatural events and battles against other spirits and gods. Yato also has a regalia named Yukine who he has to deal with as Yukine has his own growth and problems.