Will it be faster for my parents to gain citizenship if they are in the U.S. vs. being overseas? If so, what is the difference?

More convenient since they will be staying with you here during this entire process.

Can i just "transfer" my application from one eligibility to another without having to pay new application fee?

No you cannot do that. You will need to file anew and pay the fees.

Can an immigration attorney advise me please?

I agree with the colleagues. If you are traveling abroad, you should schedule Infopass appointment and ask for emergency Advance Parole.

Divorce, Green Card, Change of status.

1. F1 could take pretty long indeed. Up to 6 or 7 months. 2. No, you need to be in a valid status to apply. 3. Yes if the divorce is not final...

The receipt should come within 60 days. The actual adjudication could take many months.

Want to get indian visa for first time travel to india for baby & get oci card for remaining time in life. Is it possible?

You can try and resolve this by consulting the Indian consulate and clarifying with them.

Visit the US with 214b denial (Can apply for an ESTA)? on a Working Holiday Visa Canada - How do I visit? See below situation

You might be stopped at the border and sent back.

No. This type of liability is not included in the obligations.

One of my friend wanted to visit his relative in US and got deported since he depart at the different state.When can he reenter

If he was deported at the border it is probably for five years.

Re-entering USA as Canadian tourist soon after H1-B expiration

If you are a Canadian, you can come in on VWP and I do not think you would have problems doing so despite the H1B.