Speaking as an editor and copyeditor, you do want to be consistent. The em dash and en dash have specific uses, and a professionally edited book would never conflate them. The em dash is used for any break in thought, so the two examples you gave would both take em dashes. You wouldn't use two em dashes at the end of a sentence—it's for situations such as to indicate missing l——rs in a word. A three-em dash is used for a missing ——— in a sentence or the same author as the previous citation in a bibliography.
The en dash is used between a range of numbers (e.g., 25–30) or months (a "May–December marriage") to clarify that it's not intended as a hyphenated term. It's also used where a prefix modifies both terms of a compound expression, and hyphenation would be misleading—for example, a "pre–World War II" building (you wouldn't hyphenate proper nouns: "pre-World-War-II") or a "New York–Hong Kong flight" (you wouldn't say "New-York-Hong-Kong.") (In newspapers, you often see a hyphen used for this purpose, because journalists on daily deadlines don't have time for such niceties.)
The authority for these questions is
The Chicago Manual of Style, which is the standard reference in book publishing. Chapter 5 covers punctuation. They also have an
online version, to which you can subscribe.
As far as an em dash breaking to the next line, that's not considered a problem; in fact, it's often inevitable. In books, em dashes are closed up to the text on either side. On the web, browsers see one long word, consisting of the word on either side and the dash in between, so dashes on the web are usually open, with a space between them and the surrounding words. An ebook will behave the same as a web page, so you may get some awkward breaks, but what are the chances that two words with an em dash between them will fall at the end of a line, especially since readers can change the type size? In my books, I made the decision to keep the dashes closed up, because it's more like a print book.