Is there a way to sign into multiple Fediverse instances using the same account? Or is it possible to merge account across instances?

No and no as far as I know. But why would you want multiple accounts? Just use one account and subscribe to all the communities that are on different instances. You can even create + comment on posts with your account even if you aren't part of the instance.

The only real thing that you will miss out on is if you want to create a community on a different instance. I think you can only create communities on your local instance (Unless you sign up for an instance that restricts that feature).