1) Is it possible to make a find and replace substitution algorithm for a Quantum Computer, operate and compute hypergraphs in a quantum world rather than in traditional computer environments?

Answer: a qubit is essentially a hypergraph, where each hyper-edge (including the empty set), is labeled by a complex number. Some restrictions concerning normalization should be added, but this is easy. So, the answer to your question is "yes", but this is independent of the Wolfram Model: it is just basic quantum information theory.

2) Are there any fundamental differences between the Lambda Calculus variable substitution and rewrite process presented in the simpler string substitution and the hypergraph rewrite systems?

Answer: Because the untyped lambda calculus is Turing-complete, it can simulate the hypergraph rewrite system.

3) Is there some physical counterpart for the rewrite/substitution system i.e. what is the argumentation that rewrite is something that is supposed to go on behind the physical laws and principles and forces, is that the only computational model for doing so?

Answer: An example of the physical counterpart of rewrite/substitution is Susskind's multiway system of small unitaries: Manuscript, Video