Well they did demonstrate that in a non trivial system of axioms, there will always be true statements that are unprovable. Do they kinda accepted that they will never be able to find everything. https://en.m.wikipedia.org/wiki/Gödel's_incompleteness_theorems
Political Science is the study of political systems and behaviours employing the scientific method. It's a sub field of social science and a very new one, at less than 150 years old. Political philosophy is of course much older.
Depends. A proper computer science course is basically math with machines. At the highest level, it may have zero programming at all, and the machines in question are entirely abstract.
Software Engineering is, well, engineering (setting aside the whole debate on what makes a "real" engineer).
It used to be that universities crammed both under "computer science", and you had to look at the curriculum to figure out which one they were actually teaching. They tend to separate the two more clearly these days. Neither is really "science" in the strictest sense, but the term stuck now.
That's why informatics is by far the superior term. Computer science is such a boring terms anyways, you don't call maths "number science", biology "living beings science " or chemistry "atoms science" either.
As someone who spontaneously decided to study history / political science instead of physics, although I have been preparing to be a physicist the entire time, I can proudly say: At least I am happy. I spend most of my time doing fun and fulfilling things, instead of showing up at uni at 8 in the morning and arriving home at 8 in the evening just to work on homework. All my friends went into mint and they are stressed, don't have time to do anything and just seem the worst i have ever seen them.
Yes, Physics majors are a bit too hierachical with science like there were not doing non-rigorous math themselves but let's be honest: on the other spectrum of real/fake science it is very very hard to find actual people seriously studying the field, like you have to go up to doctorant to find the kind of serious study you find in physic undergrad.