When Ophelia asks him how his honor is, he humbly thanks her and says that he is well. We know that this is a lie because of the scene preceding this one when he is very depressed and contemplating suicide.
When Ophelia attempts to return Hamlet's letters, he denies them by saying, "No, not I. I never gave you aughtaE. He is saying that he never gave her anything and she goes on to explain how he had given her those letters and had spoke so sweetly as to make the gifts "more richaE, or more meaningful. Hamlet then laughs, maybe as an attempt to relieve the tension building between them and asks, "are you honestaE Hamlet is probably asking her if she is serious or telling the truth or he could be asking about her virtue. I think that here he is asking genuinely if she is telling the truth and then later in the scene uses its alternate meaning of virtue.
Next he asks, "Are you fairaE This word could also have a double meaning in this text. It could mean fair as in beautiful or it could mean fair as in giving proper justice. Ophelia is clearly confused by these two homonyms as she simply asks, "What means your lordshipaE He replies, "That if you be honest an