A permanent resident who is convicted of certain offenses, is subject to detention and removal from the U.S.

If you have no income, you will need a joint sponsor for the affidavit of support.

The six years start Oct '19 when you came to the U.S. as an H1b.

You could try contacting a congressman or senator's office to help intercede for you.

He can apply for the DV 23 inside the US or outside of the U.S. If he is selected and his number becomes available while he is in lawful status in...

Yes, if you wish to maintain lawful status you will need additional extension applications. Or to depart and withdraw your application.

I believe you can simply state visa was denied.

No, your leaving the U.S. will not prevent your husband from extending his L1.

If the H4 was in lawful status when the application was received, there is no issue.

You can try customer service and if that fails, you may wish to file a FOIA request.