Hey, check this out, you might find it interesting. From Parenti's Contrary Notions:

If what passes for objectivity is little more than a culturally defined self-confirming symbolic environment, and if real objectivity—whatever that might be—is unattainable, then it would seem that we are left in the grip of a subjectivism in which one paradigm is about as reliable (or unreliable) as another. And we are faced with the unhappy conclusion that the search for social truth involves little more than choosing from a variety of illusory symbolic configurations. As David Hume argued over two centuries ago, the problem of what constitutes reality in our images can never be resolved since our images can only be compared with other images and never with reality itself.

Sure, objective morality is the belief that certain actions are inherently right or wrong, regardless of individual opinions or cultural beliefs, that moral truths exist independently and can be universally recognized. The second question I haven't the slightest idea, but it would be interesting to find out.

The world would look the same way it does now with or without objective morality. Objective morality is just the idea that moral truths exist independent of individual beliefs. E.g., that raping babies is an inherently immoral thing regardless of an individual's feelings about it

Again though, I personally don't believe this. I just won't claim to know that there is no objective morality. No one can know that, the same way no one can know that there's no god, or anything else unfalsifiable

The best argument I've heard for it, from a moral philosophy professor and personal friend of mine, is (paraphrasing) "I know for a fact that genocide is inherently wrong, and I'm not open to debating that. It's just true."