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I have a generic first person character controller that I use for a lot of my games, would it be okay to use that, and then post the Unity Asset online for others to download if they wish?

Yep, that's fine!

Perfect! Is there a big list of assets, or should I just link it here? I can also start a new thread for assets

You could do it either, or publish it on the asset store. Even having it in a public github would be fine.