weak Church-Turing thesis (weak) Church-Turing thesis states every physically realizable computation device can be simulated by a Turing machine (not necessarily efficiently).
(1) Then Does any model that is not physically realizable and cannot be simulated by Turing machine?
(2) Is there any evidence for this thesis?
You are asking two questions. The answer to your first question, for models stronger than Turing computation, is the field of hypercomputation. The answer to your second question, asking for evidence for the Church-Turing thesis, has been answered on cstheory.