I don't know if we actually influence probability - perhaps once we choose something, it shows that is what was more probable all along...
As far as your #25 goes, the Talmud explains that one should learn mathematics, astronomy, and physics, if one possesses the capability, for one will see G-d's hand everywhere and one will gain a greater understanding, love, and awe of him.
The more I learn of Judaism, the more I want to learn.
All the best with you engineering studies. ...Toward a better world.