I don't know if iI will put time inton it, but iI will give it a try.

"Put time into [activity]" is the phrase

I want to practice my writing in eEnglish.

Languages are capitalized

My main goal is to be able to speak and write in fluent eEnglish.

I hope one day I willcan get thea green card to go in/move to the uUnited sStates of aAmerica, to get a brand new life and a new job.

I replaced "will" with "can" because "will" is more direct and certain
"Go" implies you're staying there temporarily, if you're planning to live there "move" would be better
Countries are capitalized

If I am one of luckiest persony people to get thea green card, I hope my girlfriend will be able to get it as well.

"Luckiest person" is singular, so you'd have to write "one of [plural noun]"
Added "be able to" for the same reason as I changed "will" to "can" earlier

I don't know if i will put time inton it but i will give it a try.

I want to practice my writing in englishEnglish writing.

My main goal is to be able to speak and write in fluent eEnglish.

I hope one day I will get thea green card to go into the uUnited sStates of aAmerica, to get a brand new life and a new job.

You haven't mentioned any specific green card yet, so it's "a green card" instead of "the green card"

If I am one of luckiest persony people to get thea green card, I hope my girlfriend will get itone as well.

I don't know if iI will put time inton it, but iI will give it a try.

My main goal is to be able to speak and write in fluent english.

To sound more fluent you would say "speak and write fluently in english"

If I am one of luckiest personthe lucky people to get thea green card, I hope my girlfiend will get itone as well.

you have to change the the object to plural when using the phrase "one of" because it means you are one of multiple (of something)

I don't know if iI will put time inton it but iI will give it a trygo.

"give it a try" is correct but I changed it as "give it a go" is more idiomatic and sounds quite natural.

I want to practice my writing in eEnglish.

My main goal is to be able to speak and write in fluent eEnglish.

I hope one day I will get thea green card to go in the uUnited sStates of aAmerica, to get a brand new life and a new job.

If I am one of luckiest persony people to be able to get thea green card, I hope my girlfriend will get it as well.