There are something i was wondering about. 

1. Why do they always take of shoes and putting on slippers? Like, it's normal in Norway also, but it's like they do it in  "a royal" way. Like it's important to respect the floor. (haha)
2. What does "arra" mean? 
3. Why do they always bow for people when they see them? If you run into that person 10 times a day, they "have to" bow? 
4. Hope i'm not being rude now. But when they eat, it's normal to eat with open mouth and talk? Here in Norway this is considering as rude. :P 

Sorry for many question, hope someone can clear this up for me, because i have been wondering about this since i watch K-dramas. :D 

1) Because that's how they do it in East Asia. (I'm from Southeast Asia, by the way, and in my country, we either use indoor slippers or just going barefoot in the house.)

2) It's an exclamation, sort of like "oh my" in English I think.

3) I guess it depends on your relationship with the other person. The more formal and/or impersonal your relationship with the other person, the more you are required, by common courtesy, to bow in acknowledgment. (Anyone can confirm/refute this?)

4) Dramatic license? And maybe it's okay when you're doing it among close friends and family?

Correct me if i'm wrong but as far as I know,

1. Why do they always take of shoes and putting on slippers? Like, it's normal in Norway also, but it's like they do it in  "a royal" way. Like it's important to respect the floor. (haha)

I think it is habitual for them to do so. Like Asian are always leaving their shoes in the entrance of the door and that is somehow traditional and habitual thing. In my country, it is actually normal in order for your feet not to get dirty and might end up cleaning the whole floor lol. So I guess for hygienic purpose and an act of habit as well.


2. What does "arra" mean? 

Arra is a shorten Araso which means I get it or I know.

3. Why do they always bow for people when they see them? If you run into that person 10 times a day, they "have to" bow?

They do that out of respect. I don't know about the Koreans but I know that Japanese will do that as long as the one they're bowing to is still doing the same to them. Basically, they need to be the last one to bow especially if they are talking to an elder person.

 4. Hope i'm not being rude now. But when they eat, it's normal to eat with open mouth and talk? Here in Norway this is considering as rude.

It has something to do with their character I guess to be able to continue speaking? Not all are doing that though. 
a little bit of reading about the culture of the country of the dramas that you're watching is probably a good idea.  you will probably enjoy the dramas more once you understand more.  I recommend wikipedia and historical websites, as well as interesting travel blogs people have written.  Every time you think of a question, look it up after the episode.  you'll find you enjoy dramas way more.
Thank you so much for answer me! Now i understand little more. 

Naksken:
I'm gonna do this :) Thanks.