Are Protogame's "worlds" equivalent to "levels" or "scenes" in other engines like Unity, or...?

Would like to know that. Also if I switch worlds in code, does the old one keeps running in the background or is its Dispose method called and it’s stopped?

When you switch worlds, the old world is disposed and it no longer runs. I recommend always using the world-related methods on gameContext to switch or create worlds.

You can only have one world running at a time.

Worlds aren’t necessarily like levels; they don’t by themselves have any functionality for loading entities from like a file (like if you use a level editor like Ogmo Editor). If you have external level files that describe the layout of your level, you’ll want to look at the Level Management module, which you can inject into your world and use to load the entities from a file.