Answer 1

If you want to work with chars:

char input = scan.next().charAt(0);

if(input == '+'){

...

}

" " -> String
' ' -> char

Answer 2

import java.util.Scanner;

Scanner scan = new Scanner(System.in);

String input = scan.next();

if(input.equals("+"){

...

}

For comparison:
primitives like int or char use ==
objects like String use .equals()