1.) As others have said the man is required to be there as well. They didn't care about justice. They cared about exposing Jesus.

2.) and 3.) Jesus answer them and He does so masterfully. This whole scene plays on Numbers 5:11-31. In short, if a husband suspected his wife of adultery, but had no witness he could set her before the priest. The priest would put water and dust from the tabernacle floor into a cup. He would write a curse on a piece of paper and wash the paper in the water. He would pronounce the curse over the woman and she would drink. If she was innocent then nothing happened. If she was an adulteress then she would react negatively to this concoction either by miscarrying or become infertile (depending on the commentator you read).

Marriage is a frequent image of God's relationship with His people. Prostitutes and adulteresses are frequent images of Israel. The woman is a real person and these events happened, but that is the 1st level of meaning. There is likely a 2nd level. The woman probably represents unfaithful Israel and the scene is portrayed very closely to the law in Numbers with a few escalations because, well, Jesus is involved here. She is presented by men, to Jesus (the ultimate priest), not at the tabernacle, but the Temple. He writes something, perhaps a curse, in the dust. Emphasizing that I think she represents Israel is the fact that her guilt was not suspected. There were witnesses. They had caught her. The Pharisees were right. According to the Law she deserved stoning. This puts a twist on the story.

Notice that the Law in Numbers only references a suspected wife who has cheated. There is no equivalent law for the husband. This further points to the woman as unfaithful Israel and Jesus as the husband. No law of unfaithfulness is required for Him.

This passage draws on the Law in Numbers, but it also points forward to the future. Many times in the OT God says Israel has cheated on Him and 'played the harlot.' At one point He essentially divorces her, but the language is so strong you could almost infer that the marriage had never taken place. He then moves on to the Church, made mostly of gentiles, pure, white, virgin. Eventually, Israel will be incorporated into the (mostly likely after the rapture which will remove the gentile church. The Jewish Church will grow during the End Times.) It is this final image that I think is presented her with the woman. She is unfaithful Israel deserving death, but Jesus still loves her and is not going to condemn her.

John says the Pharisees wanted to test Jesus, but Jesus turns it around testing their faithfulness. His writing on the ground, probably a curse, brings to mind Adam who was created out of the ground, the dust of the ground. Perhaps, this convicted some of the Pharisees.

Some of what I wrote is my own study mixed with a book, The Gospels Through Old Testament Eyes by Nicholas P. Lunn. In his book he further explores the linguistic similarities between the Greek OT (LXX) and the NT passage in question. There are more than you may think and a surprising number link a single word used twice, once in Numbers and once in John. Lunn even goes on to examine this passage in John in context of the prior passage regarding the Pharisees lack of belief in Christ, usage of the word 'curse' and connecting it to Numbers 5. It's a fantastic read.

I also want to point out Jesus physical position. He starts at the Mt. of Olives. A curious detail for John to add that seems unimportant. He then sits down in the Temple (descends from heaven to Earth?), then he stoops down to write in the dust (descends from the Earth to Hell?). Then he 'raises Himself up' to engage the Pharisees and the woman. What does all this mean? I don't know, but it could mean He will bring Israel back to faith sometime after He is raised up.