Overpopulation is only a problem in countries without the resources to feed and provide services to those people. Many countries in Europe have a very low birth rate. US is only above replacement because of constant immigration. Japan and even China is contracting.
Meanwhile you have poor countries overflowing with people that they can't even fit them in there. To show you the difference in birthrate, look at Europe now. They were only able to accommodate those refugees because they are not overpopulated themselves.
1.) The immigration of people to other countries. This depends on the person. Immigration will help other people decrease the population in a overpopulated country.
Oh, we all know how well this turns out.
Seriously though, even legal immigration would have a negative effect on the country of ORIGIN. Unless it's like in Europe where they can just walk or cross the sea to get there (in which case it becomes a free for all), most people from poor countries that manage to get to the developed ones tend to come from the better educated segment of the population. By losing these people, the country of origin become even more worse off.