Answer 1

One possibility is to iterate over your array of strings and use the compareToIgnoreCase method to order the strings (add them to another array in the lexicographically correct order).
As for Scanner input: You can find many code bits showing the usage on the playground and threads on the q&a.
https://docs.oracle.com/javase/8/docs/api/java/lang/String.html#compareToIgnoreCase-java.lang.String-