I went to onean event. I went to an event.

I went to onean event. I went to an event.

I went to oneattended an event. I attended an event.

I attended an English salon whichevent at a salon named TERAGIYA. I attended an English event at a salon named TERAGIYA.

This one was a bit confusing. If you went to an event, and the event was at a salon, then this is the correct wording. Though, with this wording, TERAGIYA is implied to be the Salon's name, not the event's name. If you went to a salon, which in the US is a business that does hair and/or nails, then "attending" would be the wrong word. The correct sentence would be: "I went to an English salon named TERAGIYA." "attending" is used more for scheduled group events, like class or like a meet-up. Even if you had a scheduled reservation for the salon, we still wouldn't use "attend," you'd still use "went to"

I attended an English salon which is named TERAGIYAeragiya. I attended an English salon which is named Teragiya.

In Japan, it's common for businesses to use katakana when they want something to stand out. And sometimes they adopt this in English or when using romaji, and use capital letters as if they were katakana, and name themselves in all caps. But capital letters are not katakana, and using all caps make you look like you're shouting. This is considered demanding and sort of rude, so even when businesses try to brand themselves in all caps, people do not use their name that way in regular speech. Their is some tolerance for weird capitalisation of company/product names (like iPad, LinkedIn, etc.) but these are the exception rather than the rule and it's usually only one or two letters rather than a whole word.

I attended an English salon which named TERAGIYA. I attended an English salon named TERAGIYA.

I added "an" before English it makes the sentence sound more natural. You don't need to include "which" in the sentence. Unsure of this salon so left it in all capitals in case that is how the salon have it.

I enjoyed studying and talking with them. I enjoyed studying and talking with them.

I enjoy studying and talking with them. I enjoy studying and talking with them.

Not sure who the "them" in this sentence is reffering to the salon its self or people also at the salon, you could replace them with who you are reffering to.

I also learned about introduction and baody condition. I also learned about introduction and body condition.

Unsure on "bady:" Did you mean "body" condition? I.e. How are you doing? I am doing fine. I am feeling sick. I am warm. I am cold. etc or, did you mean the negative / opposite condition, i.e. how to use "no" and "not" to change the meaning of a sentence to the opposite. i.e. I have a dog. vs I do not have a dog.

I also learned about introduction and baody conditions. I also learned about introduction and body conditions.

introduction = 紹介 body condition = 身体の状況 It's a weird combination, so maybe you meant something else for one of these? Since it's a salon, maybe foundation (ファンデーション) and conditioner (リンス) is my best guess?

I also learned about introduction and baody conditions. I also learned about introduction and body conditions.

Slight spelling fixes made.