The crucifixion was not a surprise to Jesus, He knew all along who He was, and the purpose for which the Father had sent Him. Some people sometimes talk about Jesus becoming aware of His ministry. Frankly, this is nonsense. The gospel's are consistent in portraying a Jesus who knew exactly who He was and what He was doing.
"He now showed the disciples the full extent of His love". This refers to all the events that were about to happen, not just the foot washing that we are about to read about, but it does include that. Jesus' love for us extends from the things of cosmic significance that He does (supremely the cross and resurrection) to much more mundane things of life, as He was about to illustrate. Our God is both Lord of All, and a God who loves each one if us in a very personal way. We need to make sure that we always keep both perspectives in view. If we just focus on the Lord of All angle we lose sight of the fact that Jesus loves me personally. If we just focus on His love for me we can end up viewing God as our personal servant!
People's feet got very dirty in those days, and washing them was a menial task. It was one best assigned to a servant or slave, definitely not to the master. In fact it was considered so menial that even Israelite slaves were not allowed to do it. So when Jesus began to ready Himself to wash the disciples feet there would be utter consternation and embarrassment among the disciples. There may also have been pangs of guilt that they considered themselves too important to wash each others feet.
The reason that Jesus felt able to do this is twofold. One, He knew exactly who He was. He knew that God had given Him all power and authority, so He had no feelings of insecurity. We too need to learn to be secure in who we are in Christ. Secondly, authority and leadership are completely different in the kingdom of God than they are in the world. In Gos' kingdom a leader is someone who serves more than others.
Peter objected when Jesus started to wash his feet, but Jesus replied that unless he allowed Him to do this he had no part in Jesus. In response Peter, in keeping with his character, went to the other extreme and asked for Jesus to wash all of him. Both of Peter's reactions were wrong. There are parts of our lives that we must allows Jesus to touch and cleanse. We all have aspects of our lives that need to be sorted out by Him, even areas of sin. We can be very reluctant to let Him do this, usually out of pride, but we must do so. Following Jesus means humbling ourselves before Him. Yet, we must not go to the other extreme, just thinking of ourselves as "unworthy sinners". If we follow Jesus then we have been cleaned, we have repented. We are not totlaly useless. A man or woman who has come to Christ is a new creation, we have the Holy Spirit within us, and God can do amazing things in and through us. But even in times when God seems to be working in and through us to a great extent, there will still be things that we need to let Him to do for us that we cannot do for ourselves. We need to keep both aspects in balance.