It seems like the only way I can add a fan page "like" button is to use UIWebView.
I personally don't like this method and I'd much prefer to be able to like the page via the Graph API, similarly to what explained here: https://developers.facebook.com/docs/howtos/publish-to-feed-ios-sdk/
In this question the last answer by ToddH was that it's possible to "like" a fan page via the Graph API. According to Stan's answer however, it seems like you can't like a fan page via the Graph API, as it's against Facebook's platform policies, but you can like via Open graph (which I haven't used yet).
In short: Can I use Graph API to like a fan page? If not is my only option is to use UIWebView (as explained in Ray's tutorial), or I have a new option to use Facebook's Open graph? (please elaborate on this option if it's legit)
EDIT: the short answer is no, you can't use Graph API/Open Graph to like a fan page. See my answer below.
Also I want to add that I don't understand why it was so important to down vote this question.