newacct

Yes, you can travel to the US. You would need to bring proof that you are the parent of your child and proof of that child's US citizenship.

The stay has nothing to do with the visa. (Like I said, visas are only for entry, and if you are not entering, you don't need a visa.) The stay is based on the I-94.

Yes. A US visa is solely for entry, and the visa is not relevant to her stay inside the US. So it doesn't matter that the visa was lost. What matters for her stay in the US is her status, as granted on her I-94. Her I-94 is probably electronic, and can be printed out. She is good to apply for extension of stay as long as she has her I-94 and has a currently-valid passport.

The immigration officers at entry do have the discretion to waive her failure to have an acceptable document for a returning immigrant. So it's possible they will let her in (perhaps with a warning), and it's possible they won't. If they won't, they could pressure her into signing I-407 to voluntarily give up her permanent residency; if that happens, she should make sure not to sign that no matter what. If she doesn't sign it, they can give her a notice to appear in removal proceedings where an immigration judge in immigration court will make a final determination on whether she abandoned residency. If the judge agrees with her that she didn't abandon residency, they will let her in. If she is trying to keep her green card, she should not try to enter on a visitor visa. (Besides, someone who has been in India in the previous 14 days won't be able to enter on visitor visa after May 4, and she doesn't meet any of the exceptions.) Keep in mind that she will need to have a negative COVID test within 72 hours of boarding her flight to the US.

1. You can travel on the GC any time up until the expiration date. To travel after the expiration date, you should get an I-551 stamp before you leave. 2. No. You should be able to get an I-551 stamp based on your pending N-400, without needing to file an I-90

You can do Change of Status inside the US. I am not sure what "didn't apply for a marriage certificate" means; does that mean you are not legally married?

Yes, by filing I-539

A child born abroad to a permanent resident mother can enter to the US as an immigrant without needing an immigrant visa, if he/she enters the US within 2 years of birth, accompanied by either permanent resident parent on that parent's first return to the US after the child's birth. See 9 FAM 201.2-3(b)(2): Airlines are allowed to board the child for travel to the US without a visa. See the carrier information guide, page 5: But if the airline won't let the child board, you may need to file I-131A and pay the fee. See the I-131A page, Special Instructions:

If her green card is still unexpired, she can fly to the US with it and try to seek entry. The immigration officer at entry has the discretionary power to waive her failure to present an acceptable document, if they determine that she has not abandoned residency. If the immigration officer does not wish to let her in, they could pressure her into voluntarily signing I-407 to give up her green card, but they have no power to revoke her permanent residency involuntarily (only an immigration judge can do that). If that happens, she should make sure to refuse to sign, and they can only give her a Notice to Appear for removal proceedings, where an immigration judge will determine whether she has abandoned residency. If they agree that she has not abandoned residency, she will be admitted as a permanent resident. The COVID situation increases the chances that the immigration officer and/or immigration judge will find that she has not abandoned residence. The alternative would be to apply for an SB-1 returning resident visa at a US consulate abroad, but to get that she would have to prove that she could not return earlier due to circumstances beyond her control. I would say that the chances of success for an SB-1 visa are lower than trying her luck with the immigration officer and/or immigration judge.

No. Adjustment of Status (I-485) is only for people who are in the US. If you want to immigrate from outside the US, you would do Consular Processing.

No. A US citizen cannot get a US visa.

Their Advance Paroles were granted before they left the US, right?

You basically can't. As you already know, unless you can get back into H1b or L1 status, she can't get a dependent status (like H4 or L2). And unless she can somehow get her own H1b or L1 status, there is no way for her to come to the US as a nonimmigrant. As long as you guys marry before you get your green card, she can still immigrate as your derivative beneficiary, but if she can't come as a nonimmigrant and do AOS, she will have to do Consular Processing as "follow to join" after you get your green card.

Officially, they immediately cannot stay anymore. However, they will not start deportation proceedings for 33 days after the date of the denial. If they think the denial is in error, they could try to reopen it; otherwise, they should leave within this 33-day period. The visa that they used to enter the US has been automatically voided. They started accruing "unlawful presence" from the date of the denial, but that won't trigger a ban unless they leave after accruing more than 180 days of unlawful presence. If they are put into deportation proceedings, that may also trigger a ban; that's why they should leave within the 33-day period. It is impossible to predict whether they will have trouble getting a visa in the future.

1. Their visa was not voided 2. No. But the immigration officer at entry can consider any factors he/she wants