Islam is the same religion which was given to Adam and all the other prophets. When It was revived by the prophet Arbaham, his progeny was chosen to hold His message and spread it to other nations. Bani Israel was a branch of his progeny chosen first for this purpose. Prophets were sent consecutively for Itmam ul Hujjah (completion of proof) to make them witness of the truth they were going to bear witness before other nations. According to the covenant of God with them, if they do not fulfil their designated job, they well be punished by God. Isa was the last of their prophets. and they were neglecting their designated duty given to them by God. So before taking the final decision against them, Isa was sent and a number of miracles were performed by them so that the children of Israel might have no excuse, no doubt that Isa was the prophet of Allah and sent before the scourge of God. His own self was made a miracle for this purpose, he took the birth without having a father.
Bani Israel is the living evidence of the living God. That is why they are mentioned at length. Moreove, Islam bases itself on the tradition of Abraham. It presents itself as continuation of the Deen which was given to Bani Israel and the coming of last episode is mentioned in the previous books especially Torah and Injeel. Islam gets its attestation from their tradition and books. That is why It says to consult their books where it is mentioned that a prophet will come with a new message from God with the same message.
Isa came at a time when the final hour of Bani Israel had come. That is why we see Jesus and his cousin prophet Yehya, did not even marry. They dedicated all their time for the warning their people. That is why, they did not have much time and variety of affairs in their life which might led them to make some mistakes, as we find the life of some other prophets.