May 21sth

As long as the pronunciation ends with "first", you will use "st".

First: 1st
Eleventh: 11th ("th" instead of "st", since "eleventh" doesn't end with "first")
Twenty-first: 21st
Thirty-first: 31st

I haunged out with 7seven of my friends yesterday.

(1) In most cases, "hung" should be used as the past tense of "hang". "Hanged" is used when referring to someone who is killed by hanging, such as in the sentence "He was hanged for murder."
(2) Since you spelt out the numbers in full in the next sentence ("five", "two"), for consistency's sake, it'd be best if you did so here as well.

We went to a Ssumo stadium called "Kokugikan" and a chanko-nabe shop for dinner, after then we went to a karaoke bar.

(1) "Sumo" is not a proper noun, and is not typically capitalised.
(2) Alternatively, you can also spell out the stadium's name in full: "We went to Ryogoku Kokugikan (National Sumo Arena)".
(3) "Karaoke" refers to the activity. Your original sentence might be acceptable in casual situations, but strictly speaking, "karaoke bar", "karaoke lounge", "karaoke box", etc. would be the location.
(4) "After then" is not a phrase that exists.

I watched Ssumo for the first time, so I didn't know how to read the program card "Bknown as "banzuke-hyou".

Alternatively, just to introduce to you more ways of expression: "I didn't know how to read banzuke-hyou, the program card."

My American friends asked me Sumo players hierarchyabout the sumo divisions.

By "hierarachy", I assume you're referring to the sumo divisions, such as makuuchi, jūryō, makushita, and so on. If you meant to refer to rankings by skill level, you can write "My American friends asked me about the sumo wrestler rankings."

However, I sometimes answeredgave the wrong answer.

(1) I'd recommend the addition of a comma.
(2) Alternatively: "However, I sometimes answered wrongly."

I (only) noticed that after I came home.

Your original sentence is okay, but I'd suggest the addition of "only" here.

My Japanese friends speak English fluenctly, but I can only speak some words or some phrases, so I thought I had to study English more.

"Fluency" is a noun. "Fluently" is the adverb.

And also, I learned a new phrases;: "other than".

(1) "And also" is okay, but I think it's more natural to just say "also" here.
(2) "Other than" is only one phrase, so "new phrases" should be singular ("a new phrase"). If you meant that "other than" was only one of several new phrases you learned, you can write: 'And also, I learned new phrases such as "other than".'

May 21sth

Some examples in which "st" is used are 1st, 31st, 91st, etc. "th" is the most common though, 2nd and 3rd are exceptions.

I haunged out with 7 of my friends yesterday.

We went to a Sumo stadium "Kokugikan" and a chanko-nabe shop for dinner, after thenat we went to a karaoke.

I watched Ssumo for the first time, so I didn't know how to read program cards "Banzuke-hyou".

Sumo doesn't need to capitalized.

(My) American friends asked me Sumo players hierarchythe hierarchy of sumo players.

However, I sometimes answered/ gave a wrong answer.

"Gave" sounds better than "answered" in this case.

I thought I had/ needed to learn more about Japanese culture.

(My) Japanese friends speak English fluenctly, but I can only speak some words or some/ and phrases, so I thought I had to study English more.

And also, I learned a new phrases; "other than".