For example, if I were to create a coin on the Waves platform, and then Waves were to go out of business, would I be able to move the coin to the Ethereum platform?
Or once you choose a platform, are you pretty much stuck with it?
I have seen coins fork into entirely new algorithms, so I imagine there is a way to do what you suggest. If I were you, though, I'd steer clear of the ETH backbone. If you want to design a token, take a look at NEM. In my opinion it works much better. I have no experience with WAVES.