1. Those are not attacks.
2. Illegal Aliens are not undocumented immigrants. Illegal Aliens have never gone through the immigration process. They migrated in not immigrated. Some illegals are documented in some ways, documentation is not the issue.
I didn't read past that line.
I don't understand what you're trying to say here. You seem to be positing a divergence between "illegal aliens" and "undocumented immigrants," as well as a dichotomy between "immigrate" and "migrate."
I have close friends who came to the United States illegally from Mexico. They are not "undocumented": they have some documents. They are not "migrants" in the sense of people moving around from here to there: they have lived here for years and don't intend to go back. They have stable jobs and are (the reason I know them) strongly contributing church members.
However, they are, in the standard phrase, "illegal immigrants" or "illegal aliens." (I think the former term is more accurate, but I understand the point of view of those who prefer the latter.) They do not go back to Mexico when, for example, a parent in Mexico dies, because they don't know if they would be able to return here. This is different from others from Mexico or Central America who are able to travel legally back and forth (if not safely, given what things are like in Mexico, Guatemala, El Salvador, etc.).