If you applied to get the visa through an I-485, then you did not do it at a US embassy or consulate.

Get a new passport, then, when you renew the F1, get the correct date of birth.

Keep following up with the National Visa Center until CIS grants the adjustment.

Not recommended, but in fact there is no rule against it.

Yes. It will take many years. No, there is no way to make it faster.

Step one is the leave the U.S. for ten years. There is a lifetime bar for multiple violators, including people who enter the U.S. illegally after...

One can file for adjustment of status based on marriage to a US citizen, if there is a pending, approved, or concurrently filed petition for alien...

There are countless possibilities. Just one example, they could become citizens of a country that qualifies for ESTA, so they won't need a visa.

She may qualify. There is no harm trying. Regardless, it seems that on November 1st, she may not need any waiver to come to the U.S., but rather...

Notify USCIS when they are back in India.