Flying is cool,
Regarding your income tax questions:
http://www.irs.gov/individuals/artic...=96623,00.html
Filing an income tax return and paying income taxes are two different animals. Many people file an income tax return every year for many years and never have to pay the IRS a dime. Myself, like most other folks, file an income tax return each year and end up owing the IRS money... go figure.
On the other hand, many people fail to file an income tax return and owe the IRS lots of money in back taxes, interest & penalties. Even "non-profit" organizations file an income tax return to remind the IRS each year that they are still a "non-profit" organization.
Keep in mind, an individual who knowingly fails to file an income tax return (or furnishes false information on their income tax return) to avoid paying income taxes is guilty of a federal offense. A regional airline may frown on this sort of activity but, I assure you, the IRS will take it very personal.
So, why do people work jobs and agree to be paid under the table? To avoid paying any income taxes. It's that simple.
Is this a crime? Yes.
Is this a serious crime? Call the IRS and ask for their opinion.
Should you disclose it? Only your integrity can answer this question.
Regarding your criminal record:
Your criminal record is public information and the airline industry has a legitimate reason to investigate you and your criminal convictions as a part of the due diligence process to pre-screen you as a potential airline industry employee.
Does this mean the airline HR people sift through multiple police reports and rap sheets from would-be pilot applicants to determine who's going to get hired? I don't know the answer to that one.
I would imagine the airline will ask you about your criminal past, if any. You then provide your information. The airline submits your fingerprints to the FBI and the Feds provide a report about your past arrest/conviction history. If the information is consistent with your answers and you're not ineligible for employment otherwise, you might get hired. If the information from the Feds conflicts with the info you provided, then I would imagine you have some explaining to do and you don't hired or you get fired after you are initially hired.