There may be times where you would pause for emphasis. In both examples, I would put more spoken emphasis on the verb and pause before the word ‘that’. Then it would be more like: I KNOW (pause) that she is from Korea. While in these examples the word ‘that’ is not strictly necessary, it isn’t incorrect and it does make a sentence slightly more formal and so more weighty and emphatic.

There are different types of THAT clause. 1. I think that she is from korea. (like your examples) This "that" is not very necessary. Very often, people just don't say it. No need to pause. 2. The language that you grow up speaking is Korean. This "that" is optional. If you really want to pause, pause before "that". 3. I like the horse that ran the fastest. This "that" is necessary in the sentence. If you really want to pause, pause before "that". Im not native though. Hopefully there will be better answers.

No pauses. Also “I know that many of people...” is wrong. “I know that many people like reality TV, but I hate it” (Pause at the comma)

I am not sure that any pause is needed in these sentences.