The assumptions don’t control the outcomes as the assumptions in Biblical interpretation do. That is why you can take the Bible and end up with hundreds of different conclusions. Each conclusion started with slightly different assumptions.
Yes there are disagreements between scientists and sometimes those disagreements end up with new science. I have never seen a Calvinist convince an Arminian they were wrong, or vice-versa.
Depends on what you mean by “historical sciences.” Geology is certainly one historical science and yes it does make predictions that are tested all the time. Otherwise geologists wouldn’t never be able to find oil and gas.
You might want to take a look at this and see why the Big Bang Theory counts as a scientific theory.