No, it did not. There has been a lot of discussion on the topic, but the reality is that he is still the Heir Apparent to the Throne. The rules regarding marriage and divorce have greatly relaxed over the years.
princess Diana is married to prince Charles
Yes, your divorce will not affect your status. However, the divorce may affect (or delay) your chances of obtaining citizenship
Possibly, assuming your permanent residence status was granted due to your marriage to a US citizen or foreign national who also is a permanent resident.
If an undocumented (illegal) immigrant is married to a U.S. citizen, then they are a U.S. citizen. So their divorce from another U.S. citizen won't affect the status of their child at all.
Married
they are back together
As a U.S. citizen, you would divorce your immigrant husband in exactly the same way that you would divorce a spouse if he was a citizen. I am not sure from your question, but if your husband's green card status is still pending, then divorcing him during the process will affect this application. If your husband was granted a conditional green card, his permanent residence privileges may be revoked if he is divorced within two years from the date this status was granted.
Still divorced.
As regards What?
no
Divorce or married single your in a relationship
NO. The day that your divorce becomes final your filing status become single unless you have a qualifying dependent living with you then you could qualify for the head of household filing status.