Netherlands & Spain don't allow it. (Spain has some exception, countries with which it's allowed.)
In Germany you have to get a special permission to retain your citizenship before you obtain another one.
Of course the names don't match... That's very common especially with women. My current legal name also doesn't match my birth name because I took my husband's surname. Your birth certificate always shows your birth name. The fact that you were born with that name doesn't change even if your legal name does.
It would make no sense to grant the extension of a TOURIST stay after they demonstrated clear immigrant intent. Since I-485s were filed for them, there was no need to file for the extensions, anyway.
You don't. Only people who were BORN in the US have US birth certificates, by definition... Also, you're still a Greek citizen, I'm not sure why you think you aren't.
USCIS will issue a NOIR (Notice of Intent to Revoke) but it will take quite some time for that. Then you need to refute their reasons (a lawyer could help).
Ideally, USCIS would then re-affirm the petitions and send them back to NVC & the Consulate.
Then it would be up to the Consulate once again.
The kids will age out, most likely, anyway. A few decades' wait before the PD becomes current and NVC needs the I-864 and by then the required income levels will change.
I guess if it was DCF the Consulate could have just ignored the need for an I-864? I definitely don't think that'd ever happen if the case was normal consular processing.
I'm assuming it wasn't an immigrant visa? To be granted a spousal visa you need an I-864. Without proven US based income or a joint sponsor or assets, no-one gets a spousal visa.
No, you need a joint sponsor or enough assets.
I don't mean to doubt your story but this was no different in 2019, so maybe your recollection is not 100% accurate?