Advance parole question

I filed forms I-130 and I-485 for my mother about 5 months ago. She is
currently in the US and has already taken the fingerprints. My mother will
need to leave the US in 4-6 weeks and I plan to file form I-131 to get her
advance parole. My questions are:

1. Does the advance parole stop the green card process, or does the INS
continue to process her applications? If the process is stopped, do we need
to ask the INS to restart it when my mother returns to the US?

2. Is the advance parole required to show at departure time? I mean, if her
departure date approaches and the INS has not responded to the I-131, should
we delay her departure until we hear back from the INS?

Thanks.

-Ayman