Green Card through Children

My father is a green card holder (five years, three months now). He has spent 33 months in the US in the last five years and for 6 months every calendar year. The issue is that on two of his most recent trips, he was out of the US for nine months, six weeks, and 11 days.

He has always been retired and has not held a job in the US or abroad. His daughter and family continued to stay in the US during these trips. He does not own a house in the US but stays with his daughter and her family and continues to have access to that residence during these trips. He does own property in India and has continued to hold that same property over the last five years. His trips abroad were to visit his other children.

What are the rough chances of "rebutting the presumption of break of continuous presence", if he applies for naturalization, despite these two trips of 9 months and 6 months two weeks ? Would you recommend going through a lawyer ?

Regarding the 9-month absence that is being questioned, if he doesn't own a house but still has access to the residence, it should be acceptable as long as there's a valid explanation for his absence of more than six months. This situation has occurred before. For example, if he couldn't return due to reasons like COVID-19, health issues, or similar circumstances, as long as these reasons are clearly explained, it should be acceptable.

My cousin’s family relocated to India from the US. They have a US-born daughter who is a US citizen.
Now the daughter wants to come back and study for a bachelor's in the US. Once she turns 21, can she sponsor the Green Card for her parents? If so, I would like to know details about the process and timeline involved.
 

Would there be any issues with parents reentering the country after filing for GC application? Say the parents entered the US on a B1/B2 visa but applied for GC while they were visiting (not for the first time). They were going to file for it once they were back in the home country anyway, but decided to submit the application now than at a later date due to some health situation that came up during the visit.

Are there chances of the application being denied/or will the parents not be allowed to reenter the country because there have been some medical emergency that happened during the visit? Should those factors need to be addressed before exiting the country before the 6 months stay time is up? And would it still be a problem if that has been addressed with the provider, given it will all be in the history file now? Would there be some state assistance that anyone can get some help with in terms of financial and patient well-being and all?
 

I am a U.S. citizen and I had applied for a green card for my parents and they were in the USA and now they have received their Advance Parole.

1. When our parents have Advance Parole, is there any special process to leave the U.S.?

2. Do we need to inform the airline staff during their check in process?

3. Even though Advance Parole documents specify that parole is valid for one year, is there any advisable timeline they could stay in India on Advance Parole?

4. What is the process for entering the USA on Advance Parole besides showing their parole documents to the CBP (Customs and Border Protection) officer at the airport?

5. Any instructions or guidelines for using Advance Parole?

6. What if their Green card gets approved while they are in India?

I am a US citizen turning 21 next month. Can I sponsor my dad to get a green card even if I am not holding his last name?

I am filing GC for my mother who is in US on visitor visa & her I-94 got extended for another 6 months. She never used her surname on her Indian passport? What should I mention in the last Name on I-130 & rest of the forms (I-485).Should I mention NA or not used or leave them blank?