Did the companions of Prophet Isa (P.B.U.H) stay devoted and truthful to the original message or did they corrupt it? (During and after the life of Prophet Isa (P.B.U.H))
The Holy Quran is silent over this question like many other details of Jesus' life. The only information that Quran gives us about Jesus' disciples is that they vowed to support Jesus in spreading religion, (3:52, 61:14), they became inspired by Allah (5:111), and they asked Jesus for a meal from heaven, as a miracle that would strengthen their faith (5:112-115).
According to the Bible's narrative, one of the disciples, Judas Iscariot betrayed Jesus to the Romans and Jewish Pharisees, and as a result Jesus was crucified.
But Quran explicitly rejects the Jewish and Christian belief in crucifixion and death of Jesus, and states that both Jews and Christians have become confused about Jesus' fate:
and for their saying, ‘We killed the Messiah, Jesus son of Mary, the apostle of Allah’—though they did not kill him nor did they crucify him, but so it was made to appear to them. Indeed those who differ concerning him are surely in doubt about him: they do not have any knowledge of that beyond following conjectures, and certainly, they did not kill him. (4:157)
Quran does not state whether there was a betrayal or not, or whether the disciples stayed faithful to Jesus or which of them did or didn't.
But in Tafsir al-Noor al-Thaqalain, there's an interesting hadith from Imam Muhammad al-Baqir (the 5th Infallible Authority for Shias and a renowned scholar for Sunnis) which provides a revealing account of Jesus' last moments with disciples and the events afterwards, which exactly answers your question. According to this hadith, one of the loyal disciples was arrested in mistake for Jesus in a miraculous Divine craft, and the other disciples were foretold to split into three groups. Two would falsify Allah (by deifying Jesus as we know) and would thus be damned to hell. The other group would stay truthful about Allah and would go to paradise. Here is the full text of the hadith in English:
Jesus foretold his companions in the night that Allah raised him to heaven (or alternately: Jesus foretold his companions the night that Allah would raise him to heaven). And they gathered around him in the evening and they were twelve. He took them to a house, and then he came out of a well that was in the corner of the house while water was pouring down from his head. The he said: “Allah revealed to me that he would raise me to Himself in a moment and purify me from Jews. Which of you shall my image [face] capture so that he would be killed and crucified [instead of me] to then join my ranks [in heaven]?” A young man among them said: “I [volunteer,] O Spirit of Allah! “ Jesus said: “[So] you are that.” Then Jesus told them: “And there is someone among you who will disbelieve in me twelve times before the dawn.” And a man among them told Jesus: “Will I be that person, O Spirit of Allah?” Jesus replied: “Do you [already] sense that in your heart? Then you will be that person.” Then Jesus told them: “It wouldn’t last long after me until you will split into three groups. Two of the groups will attribute falsehood to Allah [that Jesus is God?] and will end in hell. The other group will follow Simon and they will be truthful about Allah and thus they will be in paradise.” Then Allah raised Jesus to Himself from the corner of the house and they were looking at him. Jews came after Jesus the same night. And they arrested the young man who was captured by Jesus’ image and they killed and crucified him. And the man Jesus had foretold would disbelieve him twelve times before the dawn disbelieved.
Post-script: I realized that the authenticity of the above hadith is disputed among Shia scholars. So don't take it at face value! There's a theory (although not very famous) that this hadith has been forged by some ill-intended Jews in order to obscure the truth and defame the disciples.