What is the scriptural basis that the Devil or Satan understood God's salvation plan?

I think personally a lot of people have lots of scripture and theories on it, but I think there is only one place in scripture that needs to be given to clarify this, as it quite clearly speaks for itself:

“From that time Jesus began to show His disciples that He must go to Jerusalem, and suffer many things from the elders and chief priests and scribes, and be killed, and be raised up on the third day. Peter took Him aside and began to rebuke Him, saying, “God forbid it, Lord! This shall never happen to You.” But He turned and said to Peter, “Get behind Me, Satan! You are a stumbling block to Me; for you are not setting your mind on God’s interests, but man’s.” (Matthew 16:23).

This, plus Satan's attempt to have Jesus follow him during the fasting in the wilderness, to me clearly shows he did NOT want Jesus to complete his "race" (thus the "get behind me" part). In this "race", Satan was basically in Jesus' proverbial "dust" and couldn't not stop this force from creating a way of salvation. It's seems clear from this verse Satan knew full well Jesus' death would cause this. Keep in mind, Jesus said many times he must die and rise again, and the disciples didn't understand. I think Satan understood quite clearly the first time he said it (Mark 8:31). ;)

Now, of course, whether or not Satan knew this from the beginning of the fall ("crushing" of his head) is the part really up for debate. One thing for sure is that Satan has long been trying to kill off various people of God, including God's chosen people in general (see One Face's answer), to prevent this "crushing of his head". Personally, from what I gather from scripture, it seems Satan knew about as much of Jesus coming as we know of Jesus' second coming - namely that one is coming, but not when. ;)

The Bible may not say how well Satan understood God's salvation plan, but it does tell us that Satan had his own alternative plan which gives us clues regarding his understanding.

Isaiah 14:13-14

13 For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north:

14 I will ascend above the heights of the clouds; I will be like the most High.

Revelation 12:4-9

4 And his tail drew the third part of the stars of heaven, and did cast them to the earth...

7 And there was war in heaven: Michael and his angels fought against the dragon; and the dragon fought and his angels,

8 And prevailed not; neither was their place found any more in heaven.

9 And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him.

What we see in these verses is that Satan was in heaven, fighting against God for his own plan. He wanted to rule over the "congregation" and was successful in drawing away a third of the "stars of heaven", or "angels", who were cast out with him. Based on his proximity to God and his alternative plan for God's children, I think we can safely infer that he knew what God's plan was.

In short, Satan must have understood Gods plan at least enough to know he didn't like it.

Another clue is in James 2:19

19 Thou believest that there is one God; thou doest well: the devils also believe, and tremble.

The devils believe there is there is one God; that truth was taught by the Apostles. God's salvation plan was also taught by the Apostles. Surely the devils must know and believe it too (unless they blind themselves with their pride).

Just then a man in their synagogue who was possessed by an impure spirit cried out, “What do you want with us, Jesus of Nazareth? Have you come to destroy us? I know who you are—the Holy One of God!” (Mark 1:23-24, NIV)

From the above passage, it is possible to conclude that the evil spirits did not know the exact reason why Christ came to this world. Satan and the evil spirits knew who was Jesus. They also knew that Christ would come as it was prophesied in the Old Testament. However, they thought that Christ came to destroy them but in fact Christ came to die for our sins. They did not know that they will be destroyed only at the second coming of Jesus Christ, which is revealed only latter in the New Testament (Revelation 20).

Nevertheless, even if Satan knew that Christ came to die on the cross for our sins, as it was already written in Isaiah 53, it seems Satan has limited power to thwart God's plan.

"I don't have much more time to talk to you, because the ruler of this world approaches. He has no power over me, (John 14:30, NLT)

All that Satan could do was make Jesus give up the mission. I believe that Satan was trying his best to make Jesus suffer physically and emotionally, hoping that the pain might cause Jesus to give up the mission and return back to Heaven. However, Jesus endured all the pain and suffered till the last breath.

Satan had a good idea of God's plan of salvation for men.

The first clue was the prophecy pronounced directly against him after the fall of men.

I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel (Genesis 3:15)

Then there was the sacrificial system, where lambs without blemish were offered to God as a propitiation for sin. Clearly there was a substitute offered in place of the sinful repentant men. He would have been experienced enough to know that the blood of lambs and bulls do not actually have power to take away sin.

Satan would have also seen that not all men died. Enoch and Elijah were translated to heaven, though they were born in sin. Also when he contented for the body of Moses after his death, God has power and righteous justification to take him to heaven (Jude 9).

Satan had centuries and millenniums to study the prophecies, he knew of the Son of God and knows the references made of a Divine redeemer must have been about Him.

When Jesus came to the world, Satan made amble provisions to kill Him and tempt Him, because Jesus was "the Lamb of God, which taketh away the sin of the world" (John 1:29).

When Jesus told the disciples that he would "be killed, and raised again on the third day", Peter said "be it far from thee, Lord: this shall not be unto thee". Jesus immediately recognized that this was Satan working in Peter to to counter the plan of salvation. Jesus rebuked Peter, "Get thee behind me Satan: thou art an offence unto me" (Matthew 16:21-23).