Yesterday I started talking about Jesus' debating techniques in Luke 20. This is the other half of that... if you missed it yesterday, you might want to read that first!
Second question: Those same scribes and Pharisees sent flunkies to first butter Jesus up, and then to ask Him, "Is it lawful for us to give tribute to Caesar, or not?" They must have figured that either Jesus would answer that Caesar should get tribute, thus angering the crowd, or that he shouldn't get tribute, thus opening the door for them to have him arrested. Instead, Jesus knew they were trying to trap him and answered in a way that not only demonstrated that the people should follow the law, but also taught them that whatever has an "image" of someone belongs to that someone. Although Jesus did not explicitly mention this verse, it is the logical basis for His answer; whatever has God's image belongs to God. What has God's image? You fill in the blank! The answer was so perfect that it literally shut up the people who were trying to trick him.
Third question: Some people brought a complicated story based on a rule from Deuteronomy to Jesus, trying to trick Him into being on their side on the subject of life after death. It's not really clear to be if they were trying to do away with Jesus, but they were clearly trying to trick Him. The final question they asked, "In the resurrection, therefore, whose wife will the woman be? For the seven had her as wife" was apparently meant to allow only the answer "None of them will be her wife, because after people die they are dead and gone and it doesn't matter any more." The unexpected answer, that marriage is not an issue in the afterlife, was so clear and such a good explanation that even the people who had been trying to trick Jesus commended Him on His answer and "...no longer dared to ask him any question." Once again, Jesus shuts the mouths of His opponents.
Did Jesus stop there? No, He did not. He continued by asking His own Theological question, on that from the perspective of a Christian is simple to answer, but from the perspective of one of those religious leaders must have seemed like an insoluble riddle. Anyone who still had any idea of trying to outfox Jesus by that point must have been too scared to speak another word to Him!
The whole exchange ends with Jesus cautioning His disciples to be careful around people who are always looking for approval and financial gain at the expense of others, and making a comparison with someone who was somewhere close to the bottom of the social food chain, a widow with almost no money to live on. He basically said that she was closer to God's will than rich people, obviously referring to the scribes, Pharisees, and Saducees He had been verbally sparring with.
In the course of one chapter, maybe 15-20 minutes' worth of dialogue containing three questions and answers, not only had Jesus silenced his critics and made them afraid to say another word, but He had managed to teach several critical kingdom principles to His disciples. He never stopped teaching them, even in the middle of a heated theological debate, and kept turning things around to exactly what He wanted to talk about! Is that some great debating technique, or what?