Me and my friends and I  sang a song last Saturday.

My friends and I  sang a song last Saturday.
My friends and I  sang a song last Saturday at our friends'  wedding party.  (friends can mean singular or plural in this context)
The couple is our university friends. They have seen known  each other for 11 years.
They asked us to sing a song to celebrate their wedding party.
I was so worried because it has been almost 10 years since I did performance in front of many people. (I
Even wedding ceremony was the first experience.
But I accepted their request because the couple is amongst my best friends.
I pasted the lyric on my hand so as not to make a mistake on the stage.
I was so nervous while I sang a song but the couple were crying when the song was finished.
It was a memorable experience in my life.

me and my friends  - you are definitely going to hear English speakers say "me and my friend" but the correct order is "My friend and I"

Variations on  since I did performance in front of many people

since I performed in front of many people

since I sang in front of a large group

since I did a performance in front of many people

Variations on It was memorable experience in my life.

It was a memorable experience in my life. (You definitely need a)

It was a memorable experience.

It will be one of my most memorable experinces of my life (English speakers tend to say of my life rather than in my life. Just to confuse you, we tend to say in my lifetime :-<  )

The couple is our university friends - I don't think that an English speaker would write this.

I think they would write something different

Examples

The newly weds are both university friends.

The couple are both friends from uni.  (uni is a common abbreviation)

Summary

This is very good. You have a good understanding of English syntax, the spelling is good and I have no trouble understanding what you wrote.