import java.io.BufferedReader;
import java.util.Collections;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader
For the first issue, the problem is fairly simple. oneName is a String, and myCelebrityList is a collection of CelebrityNamesFile- which means that you can only add objects to the collection of type CelebrityNamesFile.
For the second issue, your problem is that the CelebrityNamesFile class does not implement the Comparable interface. Sorting requires that an ordering is implemented for the list element type, e.g. by implementing Comparable for the class or providing a Comparator to the sort.