Yes, sister can file for an extension with acceptable reason. It is not guaranteed the extension will be approved.

Yes, you can use a Certificate of Citizenship as proof of identity AND citizenship. Get a US passport ASAP and leave the document at home!

Yes, you may live in Canada and work in US on H1B visa.

It is wise before departure, to revisit with Mexican consulate officials about with updated visa requirements.

You may proceed with your N400 application. USCIS is not a tax regulator.

You may go ahead and submit from I693 ASAP as requested by USCIS.

It's up to the 3rd country embassy or consulate if your request can be accommodated.

It is best you retain an attorney to find out, if possible, the nature, purpose and expected impact of the TSA letter.

If you fail to respond properly and timely to USCIS RFE, your application will be denied. I'm assuming USCIS has a current and updated information...

It appears your domicile has been established by other documents in the record. Submission of your marketplace health insurance card is optional.