Is there any proof that explains that some of the characters are telepathic?

Yes, there is evidence that some of the characters are telepathic. Chapter 4 is a good place to start looking for this evidence. This chapter begins with David explaining to Uncle Axel that he can communicate with his cousin Rosalind using "thought shapes." Another good example for strong proof that telepathy is the Deviant power of the group occurs in chapter 9. This chapter begins with David explaining to readers how he and the others came to discover that Petra also has their gift. He is out working when he "hears" inside of his head a demanding scream. The call is urgent and causes David pain. He begins running in the direction that he is being called to, and along the way Rosalind joins him. They both felt the call, and they discover Petra clinging on to a bush trying not to be swept away by the current. The Sealand woman is also strong evidence of telepathy. She is able to communicate across long distances to David in order to calm him and let him know what is happening. Once they meet, readers are told that she talks in regular words but then slips into "thought-forms," which are much easier for David to follow.