1. I send messages to my friends on Kakao Talk.

2. I text to my friends on Kakao Talk.
3. I send messages in group chatting rooms on Kakao Talk.
4. I chat with friends in group chats on Kakao Talk.
[Which ones are correct? Would you correct errors?]

5. I will perform in a dance contest next month.
6. I will perform at a dance contest next month.
[Which preposition can we use, in or at? Can we use both?]

7. I will perform at a school festival next month.
8. I will perform in a school festival next month.
[#7 is right. #8 is wrong. How come #8 is wrong?]

I think all of these sentences are correct. We would say a "chat room" instead of "chatting room", but calling it a chatting room is grammatically correct, if not common usage. You may use "at" or "in" in these situations. #8 is not wrong. To say you will perform in a contest or festival means you are a participant in the event. To say you will perform at the event mean you will entertain that event participants, so it depends on what you mean, in or at. Both are correct, but mean something slightly different.

PS -- In 2, I would omit the word "to" -- it's not incorrect, but in today's normal usage (unfortunately), the preposition is usually left out!

1. I send messages to my friends on Kakao Talk.

2. I text my friends on Kakao Talk.
3. I send messages in group chat rooms on Kakao Talk.
4. I chat with friends in group chats on Kakao Talk.

All of these sentences are correct and convey the meaning that you communicate with your friends on Kakao Talk through messaging or chatting.

Regarding the preposition "in" or "at" in the following sentences:

5. I will perform in a dance contest next month.
6. I will perform at a dance contest next month.

Both prepositions can be used in these sentences, but they have slightly different meanings:

- "In" is used to indicate being involved or participating in an event or competition. So, "I will perform in a dance contest" means you will be a participant in the contest.

- "At" is used to indicate the location or venue of an event. So, "I will perform at a dance contest" means you will be performing at the location where the dance contest is held.

Regarding the sentences:

7. I will perform at a school festival next month.
8. I will perform in a school festival next month.

Both sentences are correct and convey the same meaning. The use of "at" or "in" in this context depends on personal preference and could vary based on regional variations in English usage. Both prepositions effectively convey that you will be performing at the school festival.