On my opnion you should begin with this aproach:
(if you don't want to change scenes)
Create an "arena" (where your characters will fight)
Position a camera to see this arena how you want.
Now the tricky part. You need to set the arena layer and the culling mask of the camera in order that te camera will only render the arena.
Position this arena and the camera far away from your game.
Now, when you characters collide in-game.
You instantiate new prefabs in the arena (the guys who will fight).
Disable your main camera and activate the arena camera.
Or, if you want to change scenes.
There is a lot of ways to pass information between scenes.
One of them is a Singleton. Other is DonDestroyOnLoad();
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