Boy, you are really making us think with these questions. Of course that is the idea.

1. Orual starts speaking of herself as two distinct entities: Orual and the Queen. Why would she see herself this way? Is the part of her that is Orual responsible for the things she does as Queen? Are there any other literary characters you know of who have been described in terms of dual identities?

The queen seems to be the part of her that is logical and calculating. Orual writes Chapter 13: "I was the child of Glome and the pupil of the Fox; I saw that for years my life had been lived in two halves, never fitted together." I think the "Queen" is mostly the part that is the pupil of the Fox and what she calls "Orual" is the child of Glome. I think she sees herself that way because she acts differently as the "Queen." Basically, she has named the self she shows the public "Queen" and the self she doesn't show anyone "Orual." People act in that manner all the time. Although she refers to herself as two separate entities, she really isn't so she is still responsible for her actions. Assuming that Orual is her more emotional side, Orual does influence the "Queen's" actions, for example when she lets Fox go, she "Orual" interferes when she asks if he means to leave her.

2. What can we make of the fact that Arnom doesn't seem as "holy" as his predecessor? Is this good or bad? What does it tell us about Orual's view of Ungit?

I think Orual considers "holy" to be a negative thing, something oppressive and scary. She thinks of Ungit in much the same way. I think Orual likes Arnom and can't see him that way. I don't think we really know enough to say if that is good or bad. It does make it easier for Orual to deal with him.

3. In this chapter Orual sets the Fox free from his slavery. But is he really free? Should he have left for Greece? What does free mean? Is anyone really free?

Yes and no. He can no longer be held legally but he is still slave to his emotions and love for Orual. I think Orual wanted him to have more status than a slave and be safe from being sold. She didn't even think about what he would do with that freedom. "Free" is one of those tricky concepts. Technically, everyone is "free" (able) to make his/her own decisions. A slave can choose not to work but he/she will have to deal with the consequences. However, there are many restricts put on people by themselves and others that don't make them feel free.

As far as question three goes, I'm far less concerned with the whole ideal of "freedom." I think the question is trying to make a mountain out a mole-hill (no disrespect intended ). But I'm far more interested in Orual's reaction to the Fox's plan to leave Glome once he is free from slavery.

To me, it almost seemed like she guilt-tripped him into following her will (just like she did with Psyche). She probably forgot that Fox left a family behind him (he spoke of his daughter earlier on in the book).

Which raises another interesting question: Why did the Fox stay? Surely he was smart enough to see that Orual's decision was purely a selfish motive. Sort of an "I'm going to give this to you, but you can only use it as I say." Gifts like that are not gifts at all. Does the Fox love Orual, or is she merely his "stand-in for a family" while his captivity endured? What can we make of the Fox caving into Orual's complaining?

1. I think we all act this way, sort of. Who we are in public and who we are at home can seem like very different people. But I think this is more pronounced in her case, being in a position of authority. But, though we may show different faces at different times, we are still one person, and therefore wholly responsible for our actions. I haven't read anything else with characters who describe themselves this way, however.
2. Orual seems to view 'holy' as something bad and frightening, (like Ungit) therefore it would be a good thing to her if Arnom were not as 'holy' as his predecessor. Like Pattertwigs Pal said, she seems to like him, and that makes it easier for her to approach him. But I can't say whether its good or bad.
3. He's not really free, because Orual still wants him to stay. I don't know whether he should have left for Greece or not, but I think he should have tried. I think she really put him in a bad position here, forcing to choose between his family and her. 'Free', would seem to mean 'the freedom to make one's own decisions, for good or evil'. It doesn't mean you're free from the consequences, because no one is. So in that sense people are free, but in another sense they aren't. Its hard to say.

What can we make of the Fox caving into Orual's complaining?

I halfway suspect that the Fox was tempted by both the power she offered and the fact that he wasn't entirely sure he'd make it back to whatever he'd left--and it would have changed, and by then he'd talked himself out of it. It's always easier to remain still than to change position, and easier to have someone else move you than to move yourself.

1. Everyone adapts their personality to fit a certain situation to some extent. Orual embraces this concept. She thinks if she plays the part of the queen hard enough the parts of her she doesn’t like will fade away.
2. Orual doesn’t understand the gods. She thinks she they only concern themselves with humans when they want to punish us. She does think they generally care about us.
3. It’s a complicated issue with the Fox. I don’t Orual was right to try to put conditions on his freedom when he has a life back in Greece, but I still felt her pain when he was going to leave. She never saw their relationship as slave-master. She thought of him as family. Then when he wanted to leave the second he was freed made it seem like he never really cared for her she was just an assignment. Also I couldn’t believe he wanted to leave right away and not even wait to see how her fight turned out. If he cared for her he should at least want to know if she survived.