The answers you were given for the questions were correct. Here is the routine that should have happened after you were finished. Claire should have walked in, she would be surprised that you answered all the questions correctly. Then she should leave, not too long after you should leave as well. When you get back to the docks heading North, you should meet up with Claire once more. Here she will give you TM59 and then leave. After this is done, you must return back to the old man who you answered the questions from. Once you talk to him again, he should give you the Extreme Speed Dratini.He never gave me the Dratini >_<
Also, if you do not have an empty slot in your team, then you can always go back for your Dratini afterward.