Yes, you can certainly travel outside the US while your green card application is pending. To do so, you must file Form I-131, Application to Travel Documents with the U. S. Citizenship and Immigration Services (USCIS) in which you should detail all your travel plans. File this form as early as intend to travel to allow enough for processing, upon approval you can use the approved I-131 to travel for 2 years. Do not leave the US until this is taken care. Otherwise, if you leave the US without processing and having an approved I-131, the USCIS may hold that you have abandoned your green application and cancel the entire application.

See the detailed answer below.

Yes.

The USCIS will be denying your case except for if you fall under people who have some non-immigrant statuses.

Because it my dream live in America

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