What does Chaucer intend for us to learn about the knight, in "The Knight's Tale" of "The Canterbury Tales"?
Also what are the points that are important to cover when giving a concise retelling of parts III and IV in "The Knight's Tale"?
The important points in part III are that each of the principal characters have prayed to different gods, asking for their wishes to be granted. Emily is denied, and told by Diana that she must marry one or the other. But Arcite and Paloman receive equal promises from Venus and Mars, which erupts in a war amongst the gods which the leader, Jupiter, must stop. This reflects the war between the two cousins with the king, Theseus, must stop.
For part IV, Theseus has declared no deadly weapons should be used. This supports the theme of romantic love, by removing undue violence and having the battle rely on force - as in, the force of the affection. It is the gods who decide the winner, because even though Paloman is captured, the gods create an eruption on earth in order that Arcite might be wounded. This not only ensures, through Arcite's death, that Paloman will get Emily's hand (as he should have, he saw her first), but also that the death is not the result of any man. This provides Arcite and Paloman the opportunity to make up before Arcite dies, making it a happy ending:
That never word once marred their happiness,
No jealousy, nor other such distress.
Thus ends now Palamon and Emily;
And may God save all this fair company! Amen.
From this, we understand the Knight to be a virtuous and chivalrous man, who holds tightly to the code of chivalry - including honor and romantic love - as his story shows.