Does birthplace restrict powers?

I searched through the reddit, and saw people suggesting that some powers may be restricted to their own world, but I wasn't sure if this has ever been answered:

If you're born on one world (say, Lumar, but really any), can you still gain the powers of another when there? Could they go to Roshar and bond with a spren?

And further, can one person have abilities from multiple worlds? Bond a spren and also have the ability to burn metals?

Apologies if there's an obvious thread to this that I missed!