Once an applicant has evidence that the adjustment application has been accepted by the I.N.S., the applicant may go to the nearest I.N.S. district office and apply for advance parole. To request expedited processing, the applicant must be able to prove that a genuine emergency exists. No it does not. The I.N.S. will continue to process your adjustment of status application without regard for whether you have or have not applied for advance parole, or whether you have or have not traveled abroad. No you cannot.
Advance parole is only available to people who have applied for adjustment of status.
If, however, you have a valid nonimmigrant visa and you wish to travel while you are processing for an immigrant visa with a consulate overseas, you may use your nonimmigrant visa to travel.