I’ll try to speed this up. You seem to have already implied that in your mind the content of an idea is never real. Correct me if I’m mistaken.
You are mistaken. I can think about the chair in my room. The content of that idea (the chair) is then real.
So then is the real better than the non-real? Should we strive to correspond with reality? Does truth always correspond with reality? Is truth always better?
Yes, by definition truth corresponds to reality.
The term 'better' is one that compares value judgements. So it is an idea that we use to judge the world around us. But each of us has a slightly different use of that word. So, for me, garlic is better than onions. For others, it is the reverse. It has to do with our preferences.
But, since truth corresponds to reality and falsehoods do not, it is usually better to believe in truths since the decisions you then make will more correspond to reality.
What happens when a worse morality is real in the world? Is it better? Is it more true?
By definition, a worse morality would mean that the world would be worse if it was adopted.
Morality is neither true nor false. It is a value that we either have or do not.