Katharine's request to eliminate the new tax shows more harmony between the upper and lower classes than is usually present in Shakespeare. The queen wants Henry to be more generous and to not make the people pay for the campaigns in France. She doesn't ask merely out of a soft heart but because she has wisely foreseen unrest and rebellion in the people if otherwise. The king shows himself to be an inattentive leader, yet one who is content to seem generous in reducing taxes--though his actions are really reducing the more serious danger of revolution.
This scene shows that Wolsey has taken over some of the king's authority, as Buckingham charged in the previous scene, by creating a tax without consulting the king. Wolsey's underhandedness is first proven in his own words when he tells his secretary to let the people believe the tax was reduced due to Wolsey's own effort. Then, he introduces Buckingham's former employee, the Surveyor, a man who clearly has a grudge, to speak against Buckingham. Despite the queen's astute observations about the Surveyor's intentions, no one listens to her.
The reference to Richard III refers to Shakespeare's earlier play by that name, where Buckingham's father, also the Duke of Buckingham, was Richard's right hand man in his bloody struggle for the throne. After helping Richard dispatch several royal family members who preceded Richard in line to the throne, the elder Buckingham began to doubt Richard. When Richard got the throne, Buckingham asked for lands that Richard had promised him, but Richard, seeing Buckingham's doubt, executed him. The Surveyor suggests that the younger Buckingham would himself reverse this situation--rather than being punished for being loyal like his father, the younger Buckingham would rather strike first, using the pretense of loyalty to get to the king.
The queen twice shows herself to be the most generous, kind, and wise person in the scene, first asking for the people's tax to be reduced and second by noting that the Surveyor is not giving impartial evidence. All the evidence we have on her so far is of a generous person, seemingly more aware of the dangerous intentions of others than even is the king. Yet she will be the next to fall.