Question

E- = "out of, from"

Answer 1

Simply put, we emigrate from a country and immigrate to another one. If we pay attention to the prepositions, the correct sentence is:

My mother emigrated from China and came to the United States.

The first sentence is incorrect: it should use "emigrate from Canada".

The third sentence as well: it should use "emigrate from Russia".

Finally, the fourth sentence is also incorrect: it should say "immigrating to France".