1. One of the most important immigration laws that affected legal and illegal immigration is the Act of 1965. They demolished the quota for immigration which allowed for more types of people in. Many people snuck on boat and had family members create fake papers to help them.
2. If you were illegal it lowered your chances of getting a job and making a living. If you couldn't make a living then you couldn't stay.
3. Illegal immigration could be fixed by regulating the amount of people allowed in each year. You could also hire more efficient people to make green cards. People tend to get more impatient the long they have to wait. If you set up appointments and tell them they can come back on this date to get accepted then it wouldn't be much of a concern. You could also create a camp for immigrants. Have a school, hospital, lodging, etc. and make them have a safe place to stay while they wait to be verified.