Empty lines or not?

Just use blank lines where logically you want a paragraph break. Section headings naturally form paragraph breaks already so a blank line before or after them makes no difference. For other constructs such as lists leave a blank line around them if they are not considered part of a surrounding paragraph and do not leave blank line if the list is part of the surrounding paragraph.

Note that whether paragraphs are indented or not is a style choice which should be more or less independent of the markup around individual paragraphs.

• In text mode, use (one or more) empty lines between paragraphs.

• Do not use empty lines immediately ahead of display-math environments, i.e., do not start a paragraph with a display-math environment.

• Do not use empty lines in displayed equation environments. (If you load the amsmath package, having empty lines inside equation, align, etc. will throw an error.)

• Floating environments such as figure and table can -- but do not have to be -- surrounded by blank lines. Providing whitespace around these environments, i.e., placing them between text paragraphs, almost certainly makes your code easier to read.

• Using empty lines immediately before or after \part, \chapter, \section, etc. is neither required nor prohibited. It's probably a good idea, though, to use whitespace generously to improve the legibility of one's code.