Wait for correspondence from USCIS in form of RFE.

Yes you may apply for citizenship while you await the I751 processing.

If this is not applicable, you can leave the answer blank.

Depends on the type of filing and service center it is being processed at. Check USCIS case processing times for guidance.

Contact USCIS to inquire about the rescheduling. Unclear why it was done.

More information is needed about the driving incident to make a determination.

Did you use the USCIS fee calculator?

You may use the USCIS fee calculator to determine correct fees.

Yes immediately for your parents but your sibling will take 12-16 years for processing.

You may contact USCIS to have the date corrected based on approval date but given date used, you shouldn’t have an issue with travel.