Earlier quoted context omitted.
If the theoretical prediction can't be calculated until the experiment is done that motivates the choices of what and what not to approximate, is it really a prediction?
That's what Duhem-Quine thesis in the philosophy of sciences is. The thesis is that "it is impossible to test a hypothesis in isolation, because an empirical of the hypothesis requires one or more auxiliary/background assumptions/hypotheses".
Not exactly. Analytic solutions to simple problems will produce as many predictions as you want from them, and you can test them in a year, two years, or a century from then. These highly approximated calculations, in contrast, will come out one way or the other, depending on how many of which terms you add (this is especially common in quantum chemistry) - and nobody will decide on the "right" way to choose terms until they have an experiment to compare it against. That means that they aren't predicting outcomes, they're rationalizing outcomes.