ترجمة - إسبانيّ -انجليزي - Soldado EU paga para ser herido, y no volver a Irak

Try this:

An American soldier paid to be shot and not return to Iraq.
A soldier who had just come home from Iraq admitted having paid US$500 to someone to shoot him in the leg in order to prevent him from going back to the war.

Jonathan Aponte, 20, complained to the police that a thief had shot him, but changed his statement after being questioned.
Aponte would have gone back to Irak for a stay of another 8 months.

Aponte was charged with conspiracy and makiing false statements, according to the legal accusation

Hi again, David!

Let's see...

In the source text the first sentence is a headline (in a newspaper perhaps) and it is, as headlines usually are, into Present tense, so I think it should stay this way:

An American soldier pays to be shot and not return to Iraq.

Scheme and false statement are the official denomination for the crimes he committed, while conspiracy is the criminal charge for an action which has been long planned usually envolving more than two people, isn't it?
Correct me if I'm wrong, please.

For the rest, I agree, thanks.

Nope, /scheme is not a legal defination. He can conspire to do something, even if he doesn't have a fellow conspirator.

You can absolutely not say Aponte was charged with "scheme"

conspiracy and perjury?

probably leave false statements since perjury is only a legal term for giving false statements under oath in a court of law.