There was not personal insults whatsoever in my post. Sorry if it ruined your hairdo.
1. What test can I run that would tell me if an event is "predetermined" or not?
You can try to reproduce the initial conditions for the event, and see if that leads to reproducing the event. If you can always reproduce the event by reproducing its initial conditions, then it follows that the initial conditions fully determine the event.
2. How does this test work differently in "modern science" versus the other type of science?
It doesn't work differently in "modern science". It's just that since the beginning of the 20th century, a whole lot of events have been of the type impossible to reproduce at will. Eg in the double-slit experiment you famously cannot predict where the next photon will land on the screen.