Regarding the personality stuff, you should be able to find that info in papers he's written if you have access through universities/schools still. It's pretty rigorous.Peterson is not a figure for debate based upon his use of empirical data. That's one of the hats he tries to wear, but none of it has come up in anything Ive seen or read other than his personality traits explanations. I'd like to see how he defines agreeability or the other ones, but that isn't why he is being debated.
I think the multiple subject area aspect of what he does is (usually) a strength. What's the old saying? "A well rounded man is a warrior, artist and philosopher"? When you want to tackle existential issues you need to draw from many angles to support and inform. You can't be expert in all, but it's far more impactful and holistic if done well. A single lens approach to anything will only ever produce an image framed by that lens.
Whether he gets it all right or not is a different issue.