A lawyer is not required, but it would probably be a good idea to have a lawyer look at your case to see if appeal is the best decision. For example, you may have another cause of action a lawyer may see that you are not aware of, and if you appeal and lose you could harm that other cause of action.
Yes. The minimum wage in Mississippi is $7.25, which is set by federal law. There are some states that have enacted laws that set a higher minimum wage than the federal minimum, but Mississippi has never enacted any such law.
I doubt it, but it could depend on what type of job you were applying for. If it was a federal government job most of those applications require you to swear under penalty of perjury that the information is correct. However, I have never heard of anyone going to prison for lying on an application. If the employer is involving legal it is more likely they are looking at suing you for any damages they have suffered because of your lie.
You could be liable on an individual basis if you assist the company in violating the FLSA. If you refuse to comply with the employer's demands because you believe they violate the FLSA you could have a claim for retaliation if they terminate you. You should contact an employment lawyer immediately to determine if the actions actual violate the FLSA.