Programming is all about problem solving. Programming thinking refers to the way of approaching for the solution of a problem that can be further implemented and can be put as a code. It requires to think in more "Logical" way. Though you can start coding, create something and solving problems just by learning a programming language, but it will really help to learn and have some knowledge of certain topics (but not limited to) like digital design, boolean algrebra, discrete mathematics, data structure and algorithms, etc.

Learning about operating systems really helps in understanding how different small programming and different things work together to buld a whole system. There is no proper order to follow to read about this, it depends upon how quickly one can understanda topic. But if there is an order, I think one should start with boolean algebra first, then a bit of overview of what are main components of computer and how they are organise and communicate, then learn C, then other topics. Still, it depends on how you want to approach and what are your interests in general.

Maths also will greatly help. Understanding concepts of boolean algebra, digital design, discrete mathematics like sets, proposition, data structures, algorithms, etc.

Studying about Software Engineering helps in organisation and management of a whole software project, be you are working as individual, in a small team or a big organisation, whether building a proprietery software or doing open source.

Computer Science is not just about programming, it is an aspect of computer science and the purpose is to solve problems using computers, small or big and programming helps in that. Since, we are talking to a computer using programming lanugages that it understands, we need to know how they work to develop a sort of sense to convert our thoughts into executable code.