I am now in Rio de Janerio, recovered and with a little time to begin to answer your requests.
Dispensationalism is simply the doctrine that God interacts with mankind in different ways at different times. Detractors of the doctrine see it as God trying different things. But that is not the doctrine at all. Rather than trying different things, dispensationalism realizes that God is running a series of tests to demonstrate that mankind will fail under any conceivable circumstance.
Gods first test of mankind was to leave him innocent, without any knowledge of good or evil. For they were both naked, the man and his wife, and were not ashamed. (Genesis 2:25) In this test, God gave mankind only one law. Do not eat of the tree of the knowledge of good and evil. God warned them of the result of breaking this one law, that they would surely die. But they broke that one law, because they chose to believe Satans lie that God did not have their own best interests in mind. This brought about the first change in Gods dealings. And the eyes of them both were opened, and they knew that they were naked. (Genesis 3:7) Here is a distinct change, a situation that did not exist before. They were naked before, but so what? Thats just what we look like. But now they knew that they were naked. This dispensation, though short, ended with mankind being sent out of the garden of Eden, where they had everything they could wish for provided for them. Now they had to work for a living.
After expelling mankind from the garden God left them more or less up to their own devices, with no guide (that He has told us about) except their consciences. And GOD saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually. (Genesis 6:5) The earth also was corrupt before God, and the earth was filled with violence. (Genesis 6:11) So God sent the great flood, destroying all mankind except Noah and his family. So even as the first dispensation had ended with a flaming sword that turned every way, keeping mankind out of the garden, this one ended with all mankind except one family being put to death.
After the flood, God made a new law, something that had not existed before. This, again, is a distinct change. God now said, surely your blood of your lives will I require; at the hand of every beast will I require it, and at the hand of man; at the hand of every man's brother will I require the life of man. Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man. (Genesis 9:5-6) This was again a change, something that had not existed before. And mankind went out, and began to establish kingdoms. And they began to rebel against God, building a tower to reach his heaven. (Of course, God knew, as we do today, that this would not work. But they did not know this.) Up to this time the whole earth was of one language, and of one speech. (Genesis 11:1) But the LORD did there confound the language of all the earth: and from thence did the LORD scatter them abroad upon the face of all the earth. (Genesis 11:9) So this dispensation, in which God first held man responsible to administer justice, ended with their single language confounded, so they were scattered abroad upon the face of the earth.
After this, God said unto Abram, Get thee out of thy country, and from thy kindred, and from thy father's house, unto a land that I will shew thee: And I will make of thee a great nation, and I will bless thee, and make thy name great; and thou shalt be a blessing: And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed. (Genesis 12:1-3) This, again, was something new. Something that God had never done before. He took a single man and gave him a great promise. Later on, He expanded that promise, saying, Lift up now thine eyes, and look from the place where thou art northward, and southward, and eastward, and westward: For all the land which thou seest, to thee will I give it, and to thy seed for ever. And I will make thy seed as the dust of the earth: so that if a man can number the dust of the earth, then shall thy seed also be numbered. (Genesis 13:14-16) Later, He clarified this, saying, Unto thy seed have I given this land, from the river of Egypt unto the great river, the river Euphrates: (Genesis 15:18-21) And he said unto Abram, Know of a surety that thy seed shall be a stranger in a land that is not theirs, and shall serve them; and they shall afflict them four hundred years; (Genesis 15:13) Abrahams descendants forgot the promise, and descended into the hopelessness of slavery, so hopeless that they said to Moses, The LORD look upon you, and judge; because ye have made our savour to be abhorred in the eyes of Pharaoh, and in the eyes of his servants, to put a sword in their hand to slay us. (Exodus 5:21) So this dispensation ended with the promise forgotten, and even the hope of deliverance scorned.
But God indeed brought them out, and gave them a long and detailed law, with promises of blessing for those who kept it and curses for those who did not. This, again, was something God had never done before. It was new and different. But none of them kept this law. And they finally nailed the only one who ever kept it to a cross. So this dispensation ended with the only truly righteous man who ever lived hanging on a cross.
When this dispensation ended, God again did something he had never done before. He offered salvation as a free gift to whoever would believe, regardless of what nation they were from. This, again, like all the others, involves a basic change in the way God is dealing with mankind. But God has already told us how this will end. He has said that evil men and impostors will grow worse and worse, deceiving and being deceived, (2 Timothy 3:13) and that eventually, the man of sin will sit as God, in the temple of God, showing himself that he is God. (2 Thessalonians 2:3-4)
But after this dispensation is over, God has told us of another one yet to come. In Isaiah 66, He has told us that after he comes in power and glory, he will gather all Israel back to her land. The kingdom that will be established at that time is described in great detail in numerous scriptures. This is, once again, something that God has never before done.
So we have seen that God has indeed told us of a series of different times in which he did or will do things in entirely different ways. And this is the essence of dispensationalism.