An application for a green card can be very invasive; however, you have to be willing to disclose everything. If you don't, you're only hurting yourself. This is true particularly when it comes to your criminal record. When you're asked about your criminal past, assuming that the trouble you got into because of unpaid speeding fines is not significant enough to include will be reviewed as you giving false information.
If you are trying to enter another country and become a citizen or get your work visas in order, it's important that you hire the help of some immigration lawyers that can assist you. By speaking to a few different professionals, you will learn a little bit more about putting your application in and understand the laws and how to handle every obligation required of you.