a) I want English to be my second native language

The second is not correct.

I want English to be my second language. (English is not your native language -- that's why you're learning it now!)
You can also say, "I want to learn English as a second language, being I am not a native speaker.

I left out the closing quotation marks by mistake

Harry Canarri"I want to learn English as a second language, being I am not a native speaker.

This is not natural at all to my ear. You can say:

I want to learn English as a second language because I am not a native speaker.
English being my second native language allows me to travel in many countries with no problems.
If English were my

@Alphecca...
It sounds completely natural to me -- and I would be a native speaker!

I'm posting an anecdote: Before the game a coach asks players " play please such as you never played in your life"
After the game he says "pals you understood me incorrectly, I didn't asked you to play as if you never played in your life at all !"
Where are mistakes?

"This does not sound natural to the ear at all," I would say.

"Play please such as you never (have) played in your life."
"Pals, you understood me incorrectly; I didn't ask you to play as if you never played in your life at all!"

Harry Canarri@Alphecca...It sounds completely natural to me -- and I would be a native speaker!

Perhaps you will be. And perhaps your native language is not the American variety.

Thank you, AlpheccaStars.