I have read somewhere that there is no concept of hell and heaven in Judaism. The word that is translated as hell is actually the grave or pit. How far is this true?
That is 100% accurate.
The hebrew scriptures do not have a concept of hellfire to where the wicked go.
The hebrew word 'sheol' is often translated 'hell' in english bibles....here are examples of how the word 'sheol' applies in the scriptures:
The faithful patriach Job lemented that he was soon to die and said:
Job 17:17 
“My spirit has been broken, my days have been extinguished;
The graveyard (heb. sheol) awaits me
Psalm 88:3 
For my soul has been filled with calamity,
And my life is on the brink of the Grave (Heb. sheol).
*4 I am already counted among those going down to the pit (heb. Sheol);I have become a helpless man, *5 Left among the dead
Like the slain lying in a grave(sheol), Whom you remember no longer
And who have been separated from your care.
Isaiah 38:9 
A writing of King Hez·e·ki′ah of Judah when he became sick and recovered from his sickness.
10 I said: “In the middle of my life
I must go into the gates of the Grave (heb.Sheol).
I will be deprived of my remaining years.”
The writers of the hebrew scriptures spoke of 'sheol' as the common grave...the burial tomb, the place where the dead are placed. It was never a place of fire and torment for the wicked.
Note what this encyclopdie states about the teaching of 'hell'
The Grolier Universal Encyclopedia (1971, Vol. 9, p. 205) under “Hell” says: “Hindus and Buddhists regard hell as a place of spiritual cleansing and final restoration. Islamic tradition considers it as a place of everlasting punishment.” The idea of suffering after death is found among the pagan religious teachings of ancient peoples in Babylon and Egypt. Babylonian and Assyrian beliefs depicted the “nether world .*.*. as a place full of horrors, .*.*. presided over by gods and demons of great strength and fierceness.” Although ancient Egyptian religious texts do not teach that the burning of any individual victim would go on forever, they do portray the “Other World” as featuring “pits of fire” for “the damned.”—The Religion of Babylonia and Assyria, by Morris Jastrow, Jr., 1898, p. 581; The Book of the Dead, with introduction by E.*Wallis Budge, 1960, pp. 135, 144, 149, 151, 153, 161, 200.
What rules do Christians reject from the Old Testament and on what basis? It seems odd to do so since Jesus Himself had said that He came to fulfill the Law. And two different laws for two different times?
Christians should be living according to Gods righteous standards...his standards can be seen in how his laws apply under certain situation which is what the mosaic law provides.
But the mosaic law is only applicable to the people and for the time it was provided. It was to apply to the Isrealites only until the Messiah came. When he came, it was foretold that a 'new covenant' would be given.
The new covenant pertains to only 2 laws. Love God and Love your neighbour as yourself. If christians follow the 'law of the Christ' they will fulfill what God requires of them.
Besides the 'law of love', there are some mosaic laws which were carried over into Christianity, they are as follows:
Acts 15:24 
Since we have heard that some went out from among us and caused you trouble with what they have said, trying to subvert you, although we did not give them any instructions, 25 we have come to a unanimous decision to choose men to send to you together with our beloved Bar′na·bas and Paul, 26 men who have given up their lives for the name of our Lord Jesus Christ. 27 We are therefore sending Judas and Silas, so that they also may report the same things by word of mouth. 28 For the holy spirit and we ourselves have favored adding no further burden to you except these necessary things: 29 to keep abstaining from things sacrificed to idols, from blood, from what is strangled, and from sexual immorality. If you carefully keep yourselves from these things, you will prosper. Good health to you!”
There are no other mosaic laws with regard to ceremony, festival, dietry restriction, dress code etc which was given to the christians. They simply had to
Love God
Love their neighbour as they do themselves
Abstain from things given to idols
Abstain from blood
Abstain from foods which are strangled (because the blood remains in the meat)
Abstain from all forms of sexual immorality.
These laws are part of the 'new covenant' prophesied by Jeremiah. The requirements of God changed when the Messiah came because mankind could now be declared righteous by their faith in Christ, and their commitment to love their neighbour and their God.
Why are the followers of Christ, who was a Jew, called Christians and not Jews?
Jews who rejected Jesus continued to follow Moses and the mosaic law.
But Jews who chose to follow Jesus became Jesus followers and therefore were called
Christians. The Jews were required to follow Moses until the Christ came...then they should have become followers of the long awaited Messiah... but most of them chose not to for one reason or another.
Jews today are still following Moses and many are still waiting for their Messiah.
Why are the Gods of the two testaments so different?
The Gods of the two testaments are not different at all. The Hebrew scriptures speak of YHWH or Jehovah as a merciful, compassionate, loving creator. He is also describe as a 'lover of justice' and he is often maligned because he exercised his authority to execute justice.
Jesus himself spoke of Gods desire to bring complete and lasting justice to mankind... the only way justice is ensured is if God is willing to take a stance against injustice and those who cause it.
He has done that in the past as we can see from accounts in the hebrew scriptures, and he will do so again in the very near future. He is the same God and requires the same thing from us...and he will hold us accountable for our actions just as he did in the past.
Why does a Jew reject Jesus Christ? If He is not the Messiah then who is?
The jews dont believe that Jesus was the Messiah because he was put to death by the religious leaders of his day. He was charged as a fraud and a blasphemer... the jews of his day went along with the crowd in rejecting him.
But his disciples saw his miracles with their own eyes. They saw him raise the dead to life. They heard his teachings. They were 100% convinced that Jesus was the long awaited messiah because they investigated it and saw it first hand.
Others just accepted what they heard about Jesus from their religious leaders...they accepted the charge that he was a 'false' messiah.
. And thanks for doing so.
