Sorry you're going through this.
0. You remain a Lawful Permanent Resident until Immigration Judge takes it away from you. This means you continue having all benefits as GC holder until that moment.
You should absolutely respond, explaining the situation. Even if denied, at least it shows the attempt to keep USCIS up to date. Keep record of what you sent them and proof of delivery. Perhaps you can ask your divorce attorney right a statement explaining the current state of things.
They won't ask or suggest anything. You have to be proactive and refile with waiver if current I-751 is denied.
Don't you have a driver's license? Especially if it's a real ID you can easily fly with that. Don't show GC anywhere unless you absolutely need to.
Also, make sure to renew your passport ASAP. What if you must travel overseas for emergency? Many countries allow renewing passport online.
No, if you're in removal you continue being an LPR as I mentioned in point #0.
Do not show GC to employer. Use Driver's License or state ID AND unrestricted Social Security card for I-9 verification. Employers cannot force you to show GC unless you don't have unrestricted SS card and DL / state ID.
If you don't have a state ID or DL get them tomorrow.
If you don't have unrestricted SS card, go to SSA office tomorrow.
It's time to act fast. You can do it!