The reason why I want to go there is just I got to get more experience.

got은 과거형이니까 I got이라고 쓰시면 "얻었다"는 뜻이에요 "경험 얻기를 위해"를 표현하시려면 현제시제형 쓰시는게 더 자연스러워요 :)

It's so exciting to make new friends and learning other languages.
'nice to meet you'라는 문장이 있잖아요, 그 문장처럼 동사을 묘사하는 형용사가 있으면 to를 붙이는거예요.
'nice to meet you'같은 경우에는 동사는 meet이고 meet을 묘사하는 형용사가 nice이에요.
다른 말로 표현하자면 무엇을 하는 것을 묘사할 때 보통 to를 봍여요
예를 들어서:
It's so nice to travel.
It's so scary to ride rollercoasters.
It's so easy to cook.
It's so hard to fall asleep.

I felt feel too tight suffocated where I live. If I was a genius I don't wouldn't live in here. and I don't doing wouldn't do this.
'답답하다'는 정말 아쉽게도 직역하기 되게 어려운 단어예요ㅠㅠㅎㅎ 문장마다 다르긴 하지만 제 생각에는 그런 문장에서 suffocated라고 하시는 게 좀 더 자연스러워요. tight는 '답답하다'보다 흠.. 옷이 본인의 사이즈보다 너무 작어서 잘 안맞고 약간 숨이 막힐때 쓰는 말이에요 ㅎ 예를 들어서 I bought this shirt 5 years ago and now it's too tight for me.

그리고 두번째문장은요, 무엇무엇 안했을것이다 는 I wouldn't ___이에요!
여기서 안살았을것이다 = I wouldn't live in here (사실 'in'을 빼셔도 돼요 'in'은 '~안에서'라고 생각하시면 돼요! 원래 쓰신 문장이 말이 되지만 이런 차이예요: [I wouldn't live in here 이 안에서 안살았을거예요]랑 [I wouldn't live here 여기서 안살았을거예요]

If I was a were rich, I'm would helping others more.
부자였었다면 = if I were rich이요! 가능성 좀 있으면 was이라고 쓰시고, 가능성이 아~~주 낮으면 were라고 쓰시는거예요. [~였으면]과 [~였었다면] 의 차이라고 생각하시면 될 것 같네요!
예를 들어서 혹시 'If I were a boy'라는 비욘세 노래 아요?ㅎㅎ 비욘세는 여자니까 was말고 were쓰는거예요 갑자기 남자가 될 가능성이 없어서요!

그리고 do / don't / would / wouldn't 바로 옆에 ~ing을 안써요 항상 부정사만 써요^^ 잘쓰셨어요~!!

Reason why

The reason* why I want to go there is just I got more experience.**
It's so exciting to make new friends and learning other languages.
I felt/feel*** too tight constrained where I live. If I was/were a genius I don't wouldn't live in here and I don't wouldn't be doing this
If I was/were**** a rich, I'm I'd be helping others more.

*It's best to use the article "the" in front of a noun when starting a sentence this way.

**Ambiguous, try to rewrite.

***Do you currently feel this way? Use "feel". If you no longer feel tight/constrained you can use "felt".

****Optional. In my native English, I'd use the subjunctive mood in this sentence and conjugate "to be" to "were". "If I was" is fine however because not all English speakers use the subjunctive mood.