Is this your first anime? This kind of relationship isn't really rare in anime. That one character that behaves like he hates the other but secretely loves them. That's usually called a Tsundere, though I'm not sure Kuro fits that type of character. We don't know exactly how their relationship work, but Kuro seems to actually care for her.
I'm not sure it's quite 'love' at the moment, it will be of course... But right now it's sorta like having some little girl play pretend and won't leave him alone unless he plays along, and now he's found her funny and would be upset if something happened to her.
Actually, I'm pretty sure he's staying with her because he's getting something out of it: a better relationship with the Yokai. Having a bad relationship with yokai is what ultimately destroyed his last relationship (the Kappa's reaction), so he does have motive to stay with someone that is ultimately helping him become less feared. She's essentially protecting him in a way.
right? I forgot how she actually became his gf in episode 1 but since she's the MC or "main girl" it's safe to bet the show will keep lumping them together until he actually has feelings for her, that's how it usually goes
You don't need to kill something to eat their meat. Maybe they simply got chunks of meat from mermaids. But then that raises another question. It's shown in this episode that Kuro doesn't simply create new limbs, it's like the cells that were separated from him just go back. Instead of healing, it looks like time goes back in those specific spaces.
On this episode, yes, healing is time travel. On the first episode however the eaten arm grew anew. It didn't came in the form of ribbons from the belly of the beast who ate it. This shows, like many others, is inconsistent about its own logic.
But if mermaids worked the same way, then they wouldn't be able to get the meat since it would just go back to it's owner. There's the possibility that there might be a way to kill a mermaid that we dont know. My theory though is that this "turning back time" kind of heal is particular to Kuro and might have happened due the combination of the two meats.
Unfortunately no :c. Something they omitted from the anime (ch.5 of the manga) is that if something is perceived as "manmade or imaginary" (i.e. internet OCs), it cannot physically manifest because people subconsciously acknowledge that it's a fake. Steel beam Nanase is able to manifest via the internet because people actually think she's real (aka don't realize she's a fabrication).
Well that's a stupid rule that clearly needs to be changed. I label Nanase under things people want to believe. No one would believe a faceless ghost is out killing people, but it's fun to believe it so they do. Kind of like your friend's girlfriend from Canada that he doesn't have pictures of. It's fun to believe it.