I second everything in this. Generally I would expect most writers would be happy about being an inspiration to another. Of course it’s always polite to acknowledge your inspiration.
Using someone else’s original character would in my mind require explicit permission from the original author. There is of course some grey area in what constitutes an “original character”, for example I have written a couple of short bits about the childhood of Sointu Takasuo, the Eyes of Vipers. She appears in a newspaper article with a picture, so is she a canon character or an OC? I’m happy with anyone using my child Sointu and/or the ideas about the animal affinity magic, but it’s an example of the question. If in doubt, I would prefer to err on the side of caution, i.e. ask rather than not ask.
Then again, the original author may not be around anymore. If you tried to reach them and didn’t get a a response, then you probably could go with the “inspired by” function. After all, the overall SSSS setting is on loan from Minna to all of the fanfic authors. It wouldn’t seem proper to me to claim that no one may borrow anything I have written in this setting that was borrowed by me
Again that gets hazy in the case of AUs though.
If you wish to set your story to someone else’s continuum in a way that could affect that world, it’s also possible to collaborate by making a work or a series co-authored. Obviously only if the other one agrees
For example I was inspired by a story by tehta where she mentioned a runo, so I wrote the runo. I sent it to her and as she liked it, we added it as a second chapter in the story and we are now both authors. I won’t link it here because of reasons that will be apparent if you come across it
One more thing, the Saimaa Floating Town is a collaboration and free to use as a setting by anyone without asking. So far Grey has done most work on it.
