Okay, I haven't isolated the exact fault, but I can point you on the road to resolving it.
First, The Lecture — fixed-page EPUB is a largely obsolete and problematic format that should be avoided for everything but "picture page" books like graphic novels and children's books. It should be avoided for 'flowing text' books. It is not the easy or obvious solution; trying to make an e-book look like a print book is a flawed approach. Different media, different strengths and weaknesses; use methods that make the most of each. For e-books, that's reflowable.
Anyway, the faults in your doc all seem to trace to the fonts. You're using Blackadder, which is fine... but it looks as if you bolded and italicized it in Word. Word is a sloppy tool and will bold or ital any font, even ridiculous choices like Impact, by faking the style. InDesign and other pro tools don't fudge fonts around (except by scaling), and it thus has no idea what "Blackadder Italic" and "Blackadder BoldItalic" are... because those faces don't exist. (I also have no idea what "Times New Roman Nothing" is...) Especially for EPUB export and especially-especially for Kindle, you don't want crummy "free font source" fonts in your doc; you need to stay with commercially produced ones like Adobe and Google (and Microsoft). (Better yet, don't spec fonts at all, and let the e-reader and user manage those.)
So start by doing a thorough style cleanup, and get rid of any font override or definition that does not point to a legitimate, existing face. That will probably take care of problem #2, the dozens of unnamed spot overrides in your Character Style list. You should have nothing in Para or Character Styles that does not represent a clean, proper definition with no font substitutions or overrides. And every single paragraph in your document should have a specific, named style applied, with any overrides (such as for italic) applied via a defined Character Style.
All of that is fundamental good practice with InDesign. The sloppy 'fingerpainting' you can do in Word won't fly, and messy layout and poorly defined styles will often work in print or even PDF export... but EPUB export has no tolerance for hack-and-slash formatting.
So: clean up all your files so that they are fully formatted with styles. That's probably 90% of the fix. While you're doing that, consider adapting the layout to reflowable export; I can't see anything about your book from this sample that is going to demand fixed pages, or benefit from that constricted, fussy format. And unless your chapters are really large, I'd just put the whole book in one InDesign file for ease of style maintenance and export.
Happy to answer further questions and take up any problems that persist after you've done this technical cleanup.