D it is,
The federal immigration station on Ellis Island, which was first opened in 1892, then rebuilt in 1900,
processing nearly three quarters of all immigrants entering the United States in the first quarter of
the twentieth century.
(A) The federal immigration station on Ellis Island, which was first opened in 1892, then rebuilt in
1900, processing nearly three quarters of all immigrants entering the United States in the first
quarter of the twentieth century.
Incorrect as which could refer both to ellis island or federal immigration station because both are singular and what follows which is also singular. Hence there is no clear referent. (B) Having processed nearly three quarters of all immigrants who enter the United States in the first
quarter of the twentieth century, the federal immigration station on Ellis Island first opened in 1892
and then was rebuilt in 1900.
Having processed has nothing to do with the rebuilding(C) Processing nearly three quarters of all immigrants to enter the United States in the first quarter
of the twentieth century, the federal immigration station on Ellis Island first opened in 1892, being
rebuilt in 1900.
Again meaning is distorted; and being rebuilt is incorrect.(D) First opened in 1892, then rebuilt in 1900, the federal immigration station on Ellis Island
processed nearly three quarters of all immigrants entering the United States in the first quarter of
the twentieth century.
Correct, as the sentence clearly separates the non essential modifiers from the main clause(E) Of all immigrants to enter the United States in the first quarter of the twentieth century, the
federal immigration station on Ellis Island processed nearly three quarters of them, having first
opened in 1892 and rebuilt in 1900.
federal immigration station is not an immigrant.