If your wife does not have any pending I-485, then there may not be any basis for an application for an EAD or advance parole.

Since a J1 is admitted to the US. for duration of status, one does not normally file any application for extension of J1 status.

There is no law against a lawful permanent resident leaving the U.S., so yes you are allowed to leave the U.S.

I have never heard of any rule against staying out of the U.S. for the duration of your advance parole, and returning before it expires.

A pending U visa application does not prevent you from being removed from the U.S. so you may wish to try to keep you nonimmigrant visa status.

Getting a new passport does not change the I-94 date. If the CBP gave you a wrong date you can email them to request to correct it.

Some people have been able to get that by calling the jail. You may also be able to get it from the local ICE.

The short answer to your question is that yes ,it is save to leave the U.S. for a short trip abroad with one's passport and green card.

I recall the O'Hare port director in the 1990's said that of course, they know that F1's hope some day to immigrate to the U.S. That does not and...

Certainly you can withdraw the application. Doing so will not cause the Department of State to deny any passport application in the future.