No, it doesn't have to be used in conjunction with assignment. Consider:

  printf("X is %s\n", defined $X ? $X : 'undefined');
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Or:

 sub get_name
 {
   # ...
   return wantarray ?
          ($firstname, $middlename, $lastname) :
          "$firstname $lastname";
 }
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Yes and no... It is typically at it's most useful after an assignment, and it's use is that it generates a value, but that doesn't necessarily mean it needs to be used in an assignment. Others have given examples, but the essential thing to remember is that the ternary operator returns a value. if does not: It is a flow-control operator.

So, where it does need to be used is where Perl would expect a value. Assignments are one common case of that.