There is one widely published instance of a woman almost losing custody of her two children after a court-ordered genetic test returned a mismatch. Had to be pretty confusing to hear that the guy is indeed the father, but... Objection! You are not the mother of these children!

Basically, yes. But test is costly, and won't be of any help other than telling me "You're a Chimera, Harry".
Sure, Chimeras are more likely to get some diseases , like autoimmune one (because the immune system suddenly realizing your left kidney isn't exactly yours 😅), and depression (dunno why 😅).

So for now I'll just deal with my naturally multicolored body hair (dark brown, some very blond patches, and some ginger bits), and move on.
Now that I think about it... I'm a human calico 😆

At least two distinct processes. Since we don't know how consciousness emerges we can't tell if the brain stem is strictly required, so the split-brain phenomena you're probably referencing might only shows that we got two major regions for higher brain function but not two separate… "souls"?

I swear we gonna learn sooooo much about consciousness once we're able to artificially (and safely, temporarily) link two brains together.