Unfortunately I can only help you with 1, 3, and 4.
1. A citizen is a person who is legally recognized by a government as a person of that area/country.
3. Legal citizenship matters because it gives you certain right that illeagle citizens do not have, for example American citizens have a right to due process of law and a fair trail, illegal citizens are deported without trial.
4.As stated in the Constitution a birth citizen is one who is born in the U.S. and is automatically a citizen just for being born on U.S. Soil.