Hello, welcome to Scrivener!
Just to make one thing clear, this template is intended to provide a way of working in which one writes using LaTeX for the most part. It is not meant to be a tool that takes a word processing file and converts it into LaTeX for you. There are some conveniences, for sure, but you are expected to form proper syntax in the editor out of them, and LaTeX, like most plain-text markup, demands you use one clear space between each paragraph as a matter of syntax. These systems are designed to be composed using dirt basic plain-text editing tools—you definitely would not want to look at a document someone wrote that didn’t have spaced paragraphs, in a text editor! 
That said, I have designed this template to easily accommodate a quasi-word processing typing style, for those that find fully spaced paragraphs unusual. To enable the behaviour:
- Go into Section Layouts and in any layout you use that prints text, enable the Override text and notes formatting checkbox, below the mock editor. Note that each of these built-in layouts has had the paragraph formatting pre-set to visual double-spacing. That is significant.
- Head over to the Transformations pane, and enabled Convert to plain text. The default setting I’ve supplied here is what you want. This will turn that visual spacing you saw into literal spacing.
So putting two and two together: you are telling Scrivener to internally convert all unstyled text in your thesis to visually spaced paragraphs, and then the transformation setting takes any visual paragraph spacing, either from the editor or the compiler, and turns it into carriage returns.
Keep that in mind for any custom layouts you create or modify, that are meant to handle bulk paragraph body text. They will need similar paragraph spacing in order to trigger this behaviour.
And therein is how you would conditionally override this behaviour if need be! You would not probably want to have each line of your equation spaced out, for example, or code blocks if you use those. So just make sure that stuff like that is styled text, or in a special section layout for it, and that those use single-line spacing so this whitespace conversion rule doesn’t trigger.
Yeah, you could do it that way (it’s ⌥↩, incidentally), but I really wouldn’t recommend it for all of the above reasons. If you blanket convert your entire document to double-spacing you could very well damage your output and cause all kinds of headaches in the typesetting phase.
That is referring to the special paragraph line break environment, which isn’t really a paragraph as you’re thinking of it. It’s meant for significant paragraphs that have a heading, and is traditionally typeset as a run-in head, meaning the paragraph text flows off of the heading line. You might use such a thing when going over several significant points in a document.
They are used as a “sixth level” of depth by default. If you go into your Project ▸ Project Settings… and examine the “Section Types: Default Types by Structure”, you’ll see I’ve added them as the lowest level of hierarchy allowed.
By the way, as someone new to LaTeX, the wiki I linked to above is invaluable, bookmark it. Another one I’d recommend is the TeX Stack Exchange site. Unless you have some extremely niche desire, chances are any question you can think of asking has been asked there, and answered many times over. I formatted the Scrivener user manual with LaTeX, with a huge amount of help from this site. LaTeX a great tool, but it’s a lot like learning a programming language, and online communities are a great way to do so.