Yes, your card is extended for 180 days as stated in the renewal receipt

Whatever you have already submitted should be a part of your file but you should supplement it during your interview and bring originals to review

Either lawful permanent residency status or the actual EAD may have already been issued by another petition

Because you are all lawful permanent residents already your divorce should have no effect on your family's residencies and future naturalizations

You can try to file with evidence of your pending petitions. You shouldn't have to pay if the petitions are pending.

Your mom will have to wait at least 10 more years. Currently 2007 applications are being processed. Sibling petitions can take 15+ years.

Check the processing times for All Field Offices

You want to look at the processing times for All Field Offices

Yes, a week gap will not affect your visa

You should not have an issue travelling and returning on your valid L visa