I really like the world and idea of The Fairer sex story, and I tried to upload a chapter yet it needs to be approved, yet the owner hasn’t been on in like 10 months and the story hasn’t been updated in about a year, so I don’t think it’s going to happen. So am I allowed to sort of make a new story with that world as long as I link the original story and writer? Or is that not allowed. I don’t want to break the rules or be rude here...
You can actual refer to Friedman to give you ownership of the story, or have your chapter approved by a moderator. Go look into the Generals forum, you should find what you need over yonder.
I noticed you're online as I type this, so here's that Thread Approval Report. If you want to adopt the story as your own, you have to DM Friedman for it. https://forum.chyoa.com/threads/threads-approval-reports.21/
The story owner was online a couple of days before you submitted the chapter. As there are already other chapters in review for quite some time, you might need to contact the story owner to make them aware that your chapter needs to be approved. If you make a story with your own premise, I don't see any problem. Though copying the introduction without any changes or just reworded won't work without permission of the original author. Or use this thread: https://forum.chyoa.com/threads/the-new-adopt-a-story-program.172/
You can't copy the introduction of an already existing story, but if you have an original idea for a branch, maybe you can create your own story that, after reading the first chapters it happens would fit the introduction of that other story. It also has the benefit of allowing you not to follow premises of the original story that you don't like. There are many examples of individual stories that were initially created as branches of those bigger stories and later split into their own story. Of course, that only work if you want to create your own story from scratch, and you only need the introduction. If you want to split your story from one existing branch of another story in between of it, you can't do this.