Good Evening Jayden! 
It's very nice to meet you as well. 
Thank you for contacting me in a timely and for taking the time to contact customer service about the problem you experienced. 
I dialed your number and recieved no reply, but hopefully you recieved my SMS message? 
I'm sorry to hear your phone didn't ring for our class but we will see each other next time! 
In the mean time, I will correct the message you've sent me as best as I can. 


Hi. Dear Kayla. [When greeting someone, Hi is appropriate, yes, but "Dear Kayla" would have been fine by itself as this is an email (or a letter)]
Nice to meet you. This is Kim Tae-Jeong. You can call by Jayden.

I am afraid that I didn't talk with you.
Actually, I was waiting for your call at 7:10.
However unfortunately my phone didn't ring a call. ["My phone didn't ring a call" would be "My phone didn't ring when you called."]
Maybe, This situation looks like mechanic problem. ["mechanic problem" would be "mechanical problem" 
I will call the customer service center and check the problem.

Anyway, I looked at the breaking news and made a few sentences.
Could you check the my sentence? ["Check the my sentence" would be "check my sentences" meaning there are more than one sentences, making it a plural conjugation of the word "sentence"]

1) Drink Spiking is very serious global problem. [Very good]
2) I am surprised to victims of spiked drink are very a lot of people. [This sentence would need a new structure, but your words are correct so I'll re-write it in a way that makes sense: "I am surprised that there are a lot of people who have become victims of drink spiking" so here you're just moving the subject matter around so that it sounds more fluid.]
3) I hope that everyone can drink freely through strong punishment about it.
["through strong punishment about it" is sort of hard to understand but I know what you're trying to say. Because it's hard to correct this one, I'll write a similar sentence using the words you've chosen: "I hope everyone can drink freely once there are strict laws in place to punish people who spike drinks" so my sentence is much more complicated, but it is the same point that you are trying to get across.]

I pleased that I study English speaking with you. [" I pleased " should be " I am pleased" and the same with "I study" which should be "I am studying" adding the word "am" again which means something that you're doing and adding "ing" onto study, meaning something you're doing actively, also known in the US as a verb. Which is an "action word" used to describe activities such as "studying" and "walking" ]
See you next Friday. Thank you.

Jayden.

[Thank you so much for your work Jayden. You've done very well and I'm excited to see you as well!]