newacct

USCIS is self-funded, so will keep working during a shutdown. However, immigration processes that involve other departments will be delayed by a shutdown.

There is no such thing as "waiving their US citizenship". They are automatically and involuntarily US citizens, and there is no possible way for them to lose their US citizenship until they grow up and voluntarily intend to lose it. However, as long as their birth is registered within one year of birth at an Indian consulate, and they do not get a US passport, they are also Indian citizens. I think usually they would also apply for Indian passports at the same time; I'm not sure why you guys would wait. As US citizens, there is no way for them to get a green card or US visa. The only document they can get to allow an airline to board them for travel to the US is a US passport. But getting a US passport would cause loss of their Indian citizenship. Another option for them to return to the US might be to travel to Canada or Mexico first and then enter the US by land without a US passport, using only their birth certificate.

Yes, definitely. Anything you were charged with (even if not convicted) needs to be included. And any time you were arrested (even if not charged) also needs to be included.

They should contact a CBP office and get it corrected; otherwise, their AOS could be considered to have been abandoned.

If I-485 is filed while he is in status (i.e. before he turns 21) , or (since this is an employment-based category) if I-485 is filed when he is out of status but has had less than 180 days of being out of status or illegal employment since the most recent entry, his I-485 is fine and he can stay while I-485 is pending. Note that being out of status is a separate issue from aging out. He loses H4 status immediately upon turning 21, but he might not age out for immigration purposes until later, depending on the CSPA calculation.

You remain in status for 60 days after you leave your previous job, as long as your I-94 doesn't expire earlier. As long as your new H1b petition is filed in those 60 days, you are fine.

The title of this thread says "for my E3 spouse". So does that means you are the E3 principal and your spouse is an E3 dependent spouse? Your spouse would be applying for an EAD with category (a)(17); the I-765 instructions for that type of EAD does not mention anything about receipt numbers. Nor does the I-765 form ask for anything like this for this category.

Your I-485 will be denied. Adjustment of Status in your category (spouse of a permanent resident is in the F2A category, which is not in the Immediate Relative category) requires that you were in status at the time of filing I-485, and have never been out of status any time in the past. At the time you filed I-485, your previous status had already ended, and you just had a pending Extension of Status. Having a pending Extension of Status does not mean you have status. Therefore, your eligibility for I-485 depended on your Extension of Status being approved (and approved for a period of time that includes the date you filed I-485.) Your Extension of Status was denied, and therefore, you were not in status at the time you filed I-485 and you were therefore ineligible for I-485. (It should be noted that B2 extensions of status are only for 6 months at a time, so if your status ended in December 2017, even if your first Extension of Status were granted, the status granted would not have lasted until July 2018 anyway, so it still would not have allowed you to file I-485 at the time you did, unless you filed a second Extension of Status during the first 6 months, and both Extensions of Status were approved.) See Volume 7 Part B Chapter 3, section E-1 in the USCIS Policy Manual:

Yes, she can. The second Extension of Status will depend on the first Extension of Status being approved for a period of time that includes the date the second one was filed.

No. She will pretty much definitely be found to have abandoned residence.

Yes. And they cannot leave the US until they get their green card or Advance Parole, or they would automatically abandon their AOS.

It doesn't have to be filed 45 days before the end of her stay. It just needs to be filed before the end of her stay. i.e. as long as it's officially received by USCIS before her status expires. It's when her status expires, as given on her I-94. It has nothing to do with her visa. She would need an unexpired visa to enter the US, regardless of whether or not she got an extension of status during her previous stay. "Status" is only something that exists when in the US. Extension of Status extends one's status during one particular stay. There is no "status" to extend while outside the US.

Your AOS has been pending for 6 years?

yes

She can file I-539 for Extension of Status before her I-94 expires (it needs to be officially received by USCIS before the I-94 expires). It might take 3-5 months to process the I-539, so if she files not long before her I-94 expires, and she only stays for 1-2 more months, chances are that it will still be pending when she leaves, so she has no risk of denial while she is still here.