What are the basic principles of computer science?

Computer science ultimately boils down to the study of how to efficiently compute a solution to a given problem.

From here the field has a bunch of different areas that investigate aspects of this including things such as how difficult a problem is to solve, what kind of hardware is required to be able to compute a solution, the efficiency of an algorithm to solve the problem, data structures which make solving the problem more efficient, etc.

But ultimately the field is the study of efficiently in computing a solution to problems.

I (mis)understand that the question is about unifying principles of computer science

by studying the subject one is supposed to learn how to think about layered computer systems; However upon closer study each layer turns out to be of very different nature; what has the network in common with the sql database?

Well, there here are several basic fields such as algorithms / data structures / some understanding of complexity, without them one can't really understand much of anything. So these are the bricks and mortar used in the field.

This is too abstract of a question. Universities/colleges/schools have courses dedicated to the topic. Assuming that is what you are asking, check this course: https://www.coursera.org/course/cs101

Wikipedia. Google.

Principles