My english is very bad.)

Good evening.
My name is Anny. I have a big and funny family. We learn new languages. My mother learns French; my father learns Esperanto; my youngest sister German, my second younger sister Korean, and I learn English ( and Japanese but.....tsss))) My parents are very good people.

My english is very bad.)

Good at times.
My name is Anny. I have a big and funny family. We are learning new languages. My mother is studying French, my father is studying Esperanto, first younger sister - Germany, second younger sister - Korean, and I'm learning English ( and Japanese but.....tsss))) My parents are very good people.

My English is very bad.

Do no forget that languages in English  are proper nouns and need to be capitalized.  It sounds like you have a very interesting family. 

My English is very bad.)

Good at time(1).
My name is Anny. I have a big and funny family. We learn new languages. My mother studies French, my father studies Esperanto, my first younger sister studies German, my second younger sister studies Korean, and I study English ( and Japanese but.....tsss))) My parents are very good people.

(1) Not too sure what you were trying to say here. Was this supposed to be a greeting like Good Morning?

Overall good job! You're going down the right path!