No. Green Cards are normally surrendered at the oath ceremony. I have heard of it happening only one time. If the officer asks you to surrender it, just say you need it for travel. It should not be a problem.
BTW, I'll be 73 in a few months...LOL.
That is correct. I would enter the Green Card expiration date. You will get a new extension letter when you re-file. It will also extend the expiration date of the actual Green card.
1. Your status does not expire when the extension letter does. Only the evidence of your status expires. If you need evidence of your status (such as travel), you can contact USCIS to obtain an ADIT stamp in your passport which will provide evidence that you are a legal resident.
Your visa will expire no later than 7/22. It still has to be issued, delivered, and entry into the US by that date. I don't think it is going to happen.