Certain hyper-parameters (e.g. the size of the offspring generation or the definition of the fitness function) and the design (e.g. how the mutation is performed) of evolutionary algorithms usually need to be defined or specified by a human. Could also these definitions be automated? Could we also mutate the fitness function or automatically decide the size of the offspring generation?
Yes, you can also automate the choice of certain hyperparameters of the evolutionary algorithm. In this context, this process is called self-adaptation. There are different ways of performing self-adaptation (depending on the hyper-parameter that needs to self-adapt). See e.g. the chapter Self-Adaptation in Evolutionary Algorithms (by Silja Meyer-Nieberg and Hans-Georg Beyer) of the book Parameter Setting in Evolutionary Algorithms (2007).