Okay the post is very long, and follow up posts were also very long. So this will be a similarly long reply. Cookies and cream for those who made it to the end!
I would preface this by saying that I think it is normal to "judge" our friends. We all do it. Of course we do, that is why we are friends with certain people and not with others. Because we judge that Person A is a good fit for us in terms of values or interest, or we judge that Person B is someone we wish to avoid because of attitude and personality. So judging a friend is normal and I don't think you should be scolded for it.
Your friend cheated, lied and basically isn't the person you thought she was. In other words, you didn't sign up for this! You agreed to be a godparent of a child to someone you thought was genuinely in love, in a stable marriage and with parents who shared your values. Instead, you find out that everything is indeed not what it seems and you are upset.
First, can you put your emotions aside and just decide again if you wish to continue being the child's godparent? It was an informal arrangement anyway, so I was wondering if you can pull out. Of course, it is not the child's fault and it can be seen as punishing the child for the mother's sins. But if you cannot be supportive because there is just too much drama for you to handle, I think it is better to walk away before more damage is done to both parties. The child is just 5 months old and too young to remember you yet, so there is still time to pull out. And since you live quite a distance away, this can be used as a valid reason to suggest that your friend may need to find closer and thus more involved godparents.
Second, with your friend, I really do not think it is your place to help her with her vaguebooking. I think in terms of etiquette, it is not right to give unsolicited advice to an adult. I didn't read anywhere that she asked you for your opinions and help. In fact, your posts seem to imply that she likes her method just fine. It is you and your circle of friends who can't stand it. Please understand that while this is uncomfortable, it is a perfectly acceptable situation. I do have a number of emotional drama queens (of both genders) on my facebook, and their vaguebooking is so constant that people have stopped asking them what was wrong and just let the friendship drift away naturally. We can't stand it but most of us won't say anything about it either. Occasionally someone will post a reply of "shape up and grow up!", which we all privately agree with, but also agree that it is way too brutal and ineffective to say that.
Third, I do believe that you have been way too involved in your approach. I get the feeling from your posts (I could be wrong!) that you are an exceeding straight forward person who calls a spade a spade and doesn't think twice about hiding her opinions on things. This makes you a very honest person which is good, because people can always take you at face value and trust your words. But sometimes being too honest is brutal honesty, you know? And brutal honesty is rude, hurtful and unhelpful. It doesn't get your message across to your friend but instead will make her defensive. Sometimes, it may be wiser to just bite your tongue and keep your opinions to yourself.
Fourth, other friends asking you about what is going on is normal, since the drama is vague and intriguing. Given that this is soap opera drama played out in real life, I think etiquette-wise it will be best to give a reply "I really do not know what is going on myself. Perhaps you should ask her directly by sending her a private message on Facebook". Etiquette-wise and old age wisdom makes it clear that it is a bad idea share such personal information about someone else's life, even if it isn't a big secret.