I know I shit on Bellamy a lot, but I'm just really frustrated with how he went from an actual hero who did good for his people into a grumpy boy who's Manpain clouds every decision he makes. I have to disagree with you that Clarke is unfazed by her actions; I mean, she spent three months in the woods on her own because she was too ashamed of what she'd done. She had to learn to deal with the guilt. I also think the purpose of her staying in Polis for so long was to give her character time to heal and relax, but in true 100 fashion, nothing good lasts forever. You can see a little bit of her starting to forgive herself for MW in last week's episode, when she talks to Bellamy. It's not super obvious, but it's there. She's definitely still burdened by it, but I think she's learned to live with it in a way.
That's where I think the show struggles; the motivations for their actions are there, but it never goes past the most basic "I'm upset, let me gloom around for a while". The only characters who I feel have had a proper breakdown are Octavia and Jasper. Clarke hasn't, Bellamy hasn't, Monty or Raven haven't. Maybe we'll see it, maybe we won't. But at a certain point you need to give your characters a chance to breathe, and the show hasn't done that.
Becca was indeed the first commander. She altered her blood with a specific gene therapy which did two things. One, it turned her blood black, and two, it allowed her to accept the AI, or, ALIE 2.0. She put it into her neck and fell to earth to protect her creation, landing in the ruins of what is now Polis. A bunch of survivors (stayed in the bunkers maybe?) come up to her as she's wearing a suit that says "commander" on it. I've read from the writers who answered fan questions on tumblr that she then gave her gene therapy stuff to as many people as she could, because it's what allowed her to survive the radiation. I dunno. It seems kind of far fetched. Anyway, at some point the black blood became hereditary, and increasingly rare. Which then developed into the concept of "Nightbloods" and only those with the blood can accept Becca's flame (the AI}. At a certain point it stopped being scientific and started being religious.