3: prove his point by spelling out the options available with an education.
Obama talks about different professions in the speech, they aren't just limited to science or writing. This eliminates Options 1 and 2 as possibilities. Also he is not saying that you should take specific classes, but rather you should try and do your best in every class, because you never know which class may provide you with inspiration or the skills you need later in life.
In Anne of Green Gables, Anne promises Diana she'll write Tuesday night. Diana promises to haunt the post office to wait for the promised letter.
Haunt, in this context, is meant "to linger". It means to frequent a place, or be relentlessly present.