What does "get down to cases" mean?

What does "genuinely" mean? Does it have the same meaning as "really" or "seriously?"

"Genuinely" means truthfully or honestly! It also functions as an emphasis similar to "really." "Genuinely" works well here since he's emphasising the truth of the fact, as opposed to the seriousness of something. Ex: I genuinely forgot about the meeting. = I honestly forgot about the meeting. Ex: Genuinely, I've never seen a movie as good as this one before. => extra emphasis

I don't know how to understand the meaning of "irrational fear". What's "irrational" mean here?

"Irrational" means "not rational". To explain it with other words, something that is "irrational" cannot be explained with logic or reason. An "irrational fear" means a fear that has no logical reason to exist. Ex: A lot of people have an irrational fear of spiders despite the fact that most spiders can't hurt humans. Ex: My mom is afraid that I won't eat enough when I move out, but I think she's being irrational.

What does “mean it” mean? And can I replace that expression with “for real”, “really”?

In this context, "did you mean it?" has the same meaning is "are you serious?" or "are you telling the truth?" It holds a bit of a different meaning than "for real" or "really," but the effect is similar. Ex. Then everything that you said before - did you mean it? Ex. I'm sorry, I didn't mean it.

What does "bay for blood" mean?

"Bay for blood" means to demand punishment for someone or a group of people. Ex: People are baying for blood for him on social media. Ex: My classmates have been baying for blood ever since they found out I lied about something. Ex: I hope they don't bay for blood.

What's "Gimbab"?

Gimbap (or kimbap) is a Korean dish that is made with seaweed paper, rice, vegetables, and sometimes meat or seafood. Cooked rice is rolled up with seaweed paper, and various types of fillings are put inside. It is typically cut into slices and eaten as a snack or part of a meal. In terms of appearance, gimbap looks somewhat similar to Japanese sushi, although the taste is quite different.