is it ok if send my application for example today and go out of the country for vacation the next day?
and is ok also to have someone send the application for me while i m not here? more specificaly..let`s say i leave the country jan 1st, jan 10th is time to send the application, my wife send the application on the 10th while i m still outside the country, is this ok to do, or i should be here and send the application myself? anyone can give us an idea...thanks in advance....

Having someone send it for you while you are away is fine. I would have wife send it for you.

another question ...when i become a citizen, can i use both passports i mean my original country and the american one, or just the american one? i m comfused...

You can use either, but will need to use the USA passport to re-enter the USA. Some countries do not recognize dual citizenship, so once you are a US citizen, you give up foreign citizenship, for example this happens with China, so once a Chinese person becomes US citizen, then the only passport they should use is the US passport.