Correction 

Suggestion

I want to meet many friends!

Hi everyone, I'm Hyojung. 
I want to improve my English skills and I want to meet many people from around the world. 
If you are interested in learning Korean, I can teach you. So just message me!!

In addition, if you can teach me English, again message me, I would be much appreciated! 
Thank you!

I want to make a many friends!

Hi everyone, I'm Hyojung. I want to improve my English, and I want to make many international friends (or "I want to make many friends around the globe" and "I want to meet many people from around the globe")
Also, if you want, I can teach Korean to you!!
So, if you want to learn Korean, message me. 
If you want to teach English to me, message me too. (You're not supposed to start a sentence with 'and' because it's a conjunction. Another sentence suggestion is "So, if you want to learn Korean and/or if you want to teach English to me, message me")
Thank you!