What is an on the surface question and an under the surface question?
I must admit that I've never seen the terms "surface question" and "under the surface question." My guess is that they refer to two types of questions that a teacher (or student) can ask about a literary text or any topic of study.
Some questions are about the "surface" of the text. For example, you might be asked to:
a) identify the main character;
b) list the actions taken by a certain character in Chapter 3;
c) paraphrase a passage from the text (that is, rewrite it in simpler language).
Other questions ask you to go deeper, to go "under the surface" of the text. For example, you might be asked to:
a) defend (or attack) the actions taken by a particular character;
b) compare a character in the book to someone you know in real life;
c) write a new ending to a story.
Both kinds of questions are important. It is certainly necessary to go beyond what we read in books by asking and answering "below the surface" questions; we cannot do this, however, if we don't have a solid understanding of what the "surface" of the text teaches us.