What does fitness really mean?
The concept of fitness is very general. An adequate definition of fitness is hard to specify in the same way that a definition of "species" is hard to give. To be useful, scientific or technical definition of such broad concepets will often need to be so narrow that more than one is needed. A uselessly broad definition of fitness might be:

"Fitness is modeled as a utility function, where higher fitness is indicated by a higher score"

Here every important detail about whatever's fitness is being tested, how that fitness is measured, and the environment in which that fitness is determined are simply wadded up together and transformed into a different question that is no easier to answer.

The hypothetical problems you raise with various definitions are not (in essence) problems with the definitions, but problems with the definitions not being applicable to the domain in which such problems matter. You have to define your criteria for success, and then these constraints can be translated into a "fitness" function that allows the desired predictions.

Some issues that might matter are:


Are predictions about populations, or individuals.
Are predictions about dynamic fitness (snapshot at some time) or long-run steady state fitness.
Are predictions about quantitative values (like heights) or discrete values (like sex).
How do you want to present error in your predictions - p value, sensitivity/specificity, confidence interval, etc.


I'm sure this is not the kind of answer you were looking for, but I think part of your question revolves around a confusion that there is "one" technical definition for fitness. Part of the process of learning is comparing different presentations of the same concept, and realizing where they are different. A full walk over all the different ways one could evaluate and apply fitness would be a book, not a short answer. Perhaps some other people can provide good links to more detailed information.

I just found a blog posting, by Dr. John S. Wilkins, which says some of the same things. His perspective comes with a good pedigree; his PhD work was on trying to define "species" and he has authored a couple of books on the subject.