A: This will vary based on the facts and circumstances surrounding the arrest. I would recommend finding an attorney that will give you a free consultation. It wouldn't take very long and they could go through everything with you.
A: Yes, the laws concerning when a child acquires United States citizenship when born abroad are quite complex and depend on many factors. One of these factors, which applies when the basis of citizenship is linked to a United States citizen father, concerns the length of time he physically resided in the United States. I would recommend contacting a immigration attorney to discuss the specifics of your case. That attorney will need to conduct some targeted research into the specifics of your case to determine eligibility.
A: Please be aware that starting your own business inside the United States will require employment authorization, which does not automatically come when some is on an F-1 visa. While there are certain circumstances where you can obtain work authorization while on F-1, that is a separate process that needs to be applied for and approved. I would be very careful not to violate the terms of your current F-1 status by starting a business.
You will likely need to speak with an immigration attorney to see what the best way for you to maintain your lawful status while still getting you where you want to go.