“Everyone is a fixer-upper”, in my opinion, means ‘even people who seem perfect have flaws.’ Even before I came across this word, I had some experience thinking about topics related to this. People often think of other humans as ‘perfect’ beings. As a result, when they do something ‘strange’ that is different from what you expected (for example, when they accidentally break something), you’ll express your disappointment and get angry. But you shouldn’t get angry at them because “Everyone is a fixer-upper.” Throughout life, all humans make mistakes and may accidentally expose their shortcomings publicly. It's the same for you too. If you embrace other people's flaws, then they will most likely be able to understand yours as well.
Anna felt “agony” because she felt excited about the fact that she would meet many people on the coronation day tomorrow and that Arandelle would finally be opened, while Elsa felt pressure and tension from having to keep hiding her magical powers and not reveal them to the public. I have “agonic” experiences too. I've had both experiences, and it's not uncommon. I still feel them often. For example, on the positive side, I experienced agony because I couldn't sleep the night before the hacking competition started, and on the negative side, I often had worries like 'Will I be able to do well' the day before the exam, which was painful. In fact, both cases seem to have negative consequences in the end.