There could be many interesting elements in a Spider Riders fanfic. It might explore new adventures for the characters. For example, the riders could discover a new type of spider with unique abilities that help them in their battles against the Invectids. The story could also focus on the relationships between the riders, perhaps a new friendship forms or an old one is tested.
In a Spider Riders fanfic, expect to see more of the unique bond between the riders and their spiders. It might show how they communicate in different situations. For instance, in a battle, they might have a special signal or way of understanding each other without words.
The Black Cavalry, Red Cavalry, and White Cavalry in Qing Yu's year were three different armies. The Black Knights were Chen Pingping's team. They were one of the Qing Kingdom's most mysterious and powerful cavalry forces. They were famous for their surprise attacks from thousands of miles away and had very powerful combat abilities. The Red Knights were the Qing Emperor's exclusive army. They were in charge of the Qing Emperor's safety and the Jingdou garrison. Their warhorses and soldiers were donned in red armor and looked awe-inspiring. As for the White Knights, there was no relevant information in the search results provided, so there was no way to know the specific situation of the White Knights.
There's no official rule saying they can't. Since fanfiction is a product of fan creativity and is usually not part of the official franchise control. So, they can probably watch it if they come across it.
Some kamen riders could be amused. They may see the creativity of the fans in creating unique scenarios. However, they might also be a bit critical if the fanfiction strays too far from the essence of their characters.
It depends. Sometimes stories labeled as such might draw inspiration from real events but could have fictional elements added for entertainment or narrative purposes.