Pretty much every character in Shattered Crests can be linked back to me in some way. Be it things I've felt, experienced, learned, feel, view, am, etc. Some more than others, but even I'm finding new things I can relate or see in similarity each time I focus on the characters of this story.
I'll give three examples:
Vragon: probably the most like me as a personality. Someone that's rather hard on himself in comparison to others and what he does, feels he needs to do better while not doing what he should almost as if he's afraid to accept it, the way he talks is very akin to my own in real life, strategy is something I and he enjoy, and a couple of other things I could stew on. Vragon is a lot more of what I would call a "literal" relation, though I wouldn't say he's a self-insert. There's a lot about him that's different from me still and his struggles are pretty much never going to be mine, aheh.
Ciecro: Vragon used to be my favorite character in terms of relation and how he was pseudocrafted a lot like me. However, as I worked on Ciecro's character more and built his development, I gradually began to really enjoy Ciecro to the point he's now my favorite of my protagonists. His development is very similar to how I've grown as a person and where I wish to of. Someone that feels he's let people he cares about down and thus feels the need to push himself, even if the views he holds of himself are higher than he should, potentially unhealthy. Someone that cares deeply about his family and would gladly bite the hit for them. Someone that wants to help and is frustrated when he doesn't know how or can't. Someone who doesn't know where to go with his life and holds to some idea of "guidance" from someone older that can help him find his path. I could go on. It's one of the reason I like him so much besides just his personality. His struggles, choices, and character feel very "present-day" for me. If Vragon is what I would view as the "me" of years ago, Ciecro would be the "me" recently. He would be what I would call a "development" relation.
Baphomet: Is one of my favorite of the antagonists. Someone that has a backstory that's not the most depressing, but still shows his struggles. He is part of a core theme in the story, and his reaction to what he sees in this world and what he does with that reflects my own personal worldview. I don't really share much when it comes to his backstory and conduct nor physical traits or quirks, but I do share a mindset similar to him. I'll spare spoiling it for now, but I can say I would classify this as a "Exstistential" relation.
To answer your second question, I'm not really a fan of self-inserts because you can draw aspects of yourself into almost everything in the story already. So much already says so much about you. It feels like taking the "literal" way to much and can really minimize the ability of a reader to really appreciate what is said here, since oftentimes self-insert stories are written just for the self-insert person. Some can write this in ways that work very well and some go as Palamon said, "Overboard".