USCIS Service Centers are facing severe backlogs at the moment. Continue with your inquiries and consider filing for Mandamus.

Need TPS first for all the benefits you mentioned. ESL not a problem.

Check the USCIS processing times for your particular kind of application.

You will need to disclose the DV entry during the interview if asked. No big deal. Everyone applies and overwhelming majority "loses."

Whenever "decision" is mentioned, that means denial, hopefully not in this case.

Unfortunately not. Only USCIS can engage in that.

A FOIA with USCIS should also be attempted.

You can apply for the COS to F-2 anytime within your 60 day grace period.

That's nothing important as far as you are concerned - simply routine.

No - carry your valid state issued ID and/or passport instead.