2) The list of likes comes directly from FB
3) There is an endpoint provided by the Facebook Open Graph to delete a like. However, you have to be whitelisted by FB in order to call that endpoint.
4) Yeah, the thought was that you'd come here to unlike pages. If you made a mistake in unliking a page that you want to continue supporting you can go back there on FB and re-like it. The reason we removed the button after the action is that it's crazy confusing to explain to someone how to unlike a page using the default FB like implementation (the only implementation) and I'm sure that's by design. If the button stuck around after the action, I'm sure that there would be a lot of unintended re-likes.
Thanks, we're trying! Our goal is to help consumers voice their complaints to large companies (that aren't always listening too well). Please give us more feedback!
Thanks!