He is of course referring to eternal life. We continue to live on even after our earthly bodies have died.

I think he wept because Lazarus was his friend. Jesus came to experience life as a  human. Grief is part of life. And although he had the power to bring Lazarus back and did so, he still experienced loss and the pain that comes with it.

Ultimately, to show God's power before all who would be present at the raising of the dead man Lazarus. Enough time had passed that everyone knew that Lazarus was dead, no question about it. Jesus showed his power and recieved the glory for bringing Lazarus back to life.

The Lord spoke through the prophets of the Old Testament that this was going to happen. Since nothing is outside of God's control, (even Satan) he allowed Satan to enter Judas so that prophecy could be fullfilled, He allowed Judah to accept the Pharisee's money in return for Jesus. He allowed the kiss of betrayal, so that prophecy could be fullfilled and ultimately bring about Christ's death so that we (in turn) could have a savior and eternal life with the Father. It was all done out of love for us, the children of God.

I believe that because God's truth is the only truth, it was very hard for the Sadduccees to accept what Jesus told them. Instead of embracing the truth of the Resurrection and marriage, they chose to ignore it and cling to their traditions and beliefs.

Also, the Bible speaks of Jesus teaching with great authority, this probably provoked fear in the Sadducees as well.