I'm not claiming that at all. in my example the parts of the theory that use maths can be proved, they are either true or false. The parts of the theory that rely on observation or measurement cannot be proved, they are best guesses at the properties of reality that we are trying to model.
If any parts of the theory cannot be proved, the entire theory cannot be proved.
Because all empirical science relies to some degree on observation or measurement, its theories cannot therefore be proved.
Again, it depends on the parameters given.
If you give me more and more useful information, I can give you a better theory. However, if you tell me to do what Kirk told Spock to do: "Build an interstellar transmitter out of bear skin and sticks", I'll probably end up giving you something that looks like a pipe-dream gone wild.
Also, the amount of information that we have already is so large that the ratio of possibilities from a physicist's point of view to the amount of possibilities for the person running the program is absurd. Sure, you could, given enough energy (in this case provided by anti-matter annihalation), you could get to Mars in a matter of weeks. However, just producing just a tablespoon of anti-matter would bankrupt the United States of America.
As you can see, it's all about the parameters, they control the outcome. Thus, scientists try to control the parameters as much as they can; but they aren't all-powerful (which oddly enough, by its very defenition, is impossible), they're just average joes like you and me with a job that might actually pay very little at all.
-Penguin