I appreciate this kind of post. Since the community already answered your concern with examples and specifics, I'll paint my answer with broader strokes. And I'll only answer the first and last one, since I believe the second and third were explained by @owensd better than I could've.
Does version controlling my source really solve any problems?
Does build management really help creating better quality software?
Does test automation really produce better code?
Is it really air that I breathe...
Given how you actually asked these questions in the first place, you are ahead of the game (I'll explain why in just a second), and already capable of answering them. But, since you asked us, I'll give my two cents too:
Does version controlling my source really solve any problems?
It might do you well to frame "Does X solve Y" as a "What is X and what can it do" question. You'll invariably answer the former by considering the latter.
So, what is version control? A system capable of handling and tracking the changes of a collection of data —whether a document, source files, website, or any information mutating over time. It can be as simple as tracking one revision to another, or as complex as managing variable features in your project (e.g. through branches) and take them to different paths until they merge into a single one yet again. The system can be made just for a single person or to support multiple teams. So on and so forth.
Once you understand what a Version Control System (VCS) can offer, you can use it to your advantage and restrict it to the uses that you actually need. Users like @rathersleepy, @owensd, and @mmozeiki know this, and made reasonable value judgments (not in its disparaging sense) accordingly.
Is it really air that I breathe...
Heh, this is why you're ahead of the game. In my experience working with other software engineers, they tend to not question things, rarely try things out themselves or even consider ROI, and immediately default to a set of prescribed rules and principles.
This horse has been beaten to death on this forum, but it still rings true. The
"Global Variables are Evil" mentality is what keeps me up at night, reminding myself that I have to take a stand and complain when people are spending hours thinking about the code much more than they are the problem.
"Is it really air that I breathe..." questions are both funny and, dare I say, necessary.