Do we have any historical evidence that Jesus visited India? What is the evidence and the source for the belief held by many people in India that the Roza Bal shrine is the tomb of Jesus?
The recent written source for the idea that Jesus is buried at Roza Bal is here: Jesus in India - by Mirza Ghulam Ahmad - The Discovery. No forensic evidence seems to be cited. Ahmad relied on his own personal research of the subject and older Islamic traditions, oral and written.
As for Jesus visiting India during his life, See: Nicolas Notovitch: Notovitch is known for his 1887 book claiming that during his unknown years, Jesus left Galilee for India and studied with Buddhists and Hindus there before returning to Judea, although Notovitch himself (based on the wiki - I have not read the book) never claimed Jesus was buried in India or Kashmir but traveled there and then returned to Palestine. (Thanks to @LennartRegebro for this reference.)
But Notovitch is a problematic source: He later admitted that his story was essentially a fabrication, and as a European writing in Europe, it's unlikely that he was the source of those beliefs you refer to. Perhaps the writings of Swami Abhedananda: Although Notovitch had been discredited in Europe, Swami Abhedananda wrote a book called Journey to Kashmir and Tibet in which he stated that had visited Hemis and seen a document similar to the one Notovitch had mentioned, and produced a Bengali translation of parts of it, are better sources for this idea.
Regarding the validity of the claim that the Roza Bal Shrine is Jesus's tomb: In light of the extensive biblical testimony that Jesus was entombed in ancient Palestine, Resurrection of Jesus, Burial,Resurrection of Jesus, Tomb Discovery, one would need to explain how Jesus's body ended up in Kashmir. But if we accept the biblical account of the Resurrection, it is possible to say that once he was resurrected he could have ended up anywhere. But again, this is contradicted by the biblical account: His final appearance is reported as being forty days after the resurrection when he ascended into heaven[Lk. 24:44–49] where he remains with God the Father and God the Holy Spirit until the Second Coming of Christ.
Whether or not we accept the biblical account of the Resurrection, the numerous biblical references and their persistence would seem to put the burden of proof on Ahmad and his sources, and the evidence does not appear to weigh in their favor, particularly since we have other sources besides the New Testament attesting that Jesus lived and died in Palestine. If so, a very good explanation must be offered as to how his body ended up in Kashmir, thousands of miles away.
There seems to be no mention of Susan Olson and the German author Holger Kerstens book 'Jesus lived in India'. There is growing evidence to suggest that Jesus did die in India.