The song you wrote in the second link address is sung by Korean singer Kim Hyun Jung, called "Farewell with Her";

The third link address is Korean singer Lee Jung Hyun "Shake"

I don't know the first one

I also practice Taekwondo. I love listening to these three songs. In addition, at your invitation, I would like to recommend some Among the more hi songs for practicing Taekwondo, Lee Jung-hyun's "Half", "Myth", "Unique", "Ali Ali" and "Love Me"