Lots of questions. Thanks for your patience.

I'll try to answer at least some of your questions. I don't have answers for all of them.

a. Is there a way to prevent automatic unwanted format changes to  complex tables? Every time I open the document, a few tables are changed. They are too complex to be assigned one style. Is it possible that if a table has no Style, Word feels free to change its format?

In Word, just as every paragraph has some style, every table has some table style. In the same way that Normal is the default paragraph style, Table Grid is the default table style. However, table styles are flaky and have been ever since their introduction in Word 2002. Refer to Shauna Kelly's article for an excellent rant.

Although table formatting should never change just because of reopening a document, the conversion of Word's memory-resident image to the XML in the disk file could have a bug that's triggered by particularly complex formatting. If you can isolate particular tables that are unstable, I can pass them to the Word developers to investigate.

b. Why does displaying the XE fields completely change the page numbering and page layout? Can this be prevented? If not, it was a horrible design decision. They should have handled it like the Review notices off to the right.

XE fields are comparatively old constructs in Word, and they behave like all other fields -- their code displays inline. Tracked changes and comments came along later, and they use a different display mechanism. I doubt that Microsoft would consider rewriting the indexing code to accommodate your suggestion, as good as you and I think it would be.

Every XE field is automatically formatted as Hidden. You can avoid changing the layout by going to Options > Display and unchecking Hidden text. This is absolutely required before you generate the index, to avoid getting incorrect page numbers.

c. Why doesn’t Advanced Find have a backwards search or a count of instances found?

It does. To search backward, click the More button to expand the dialog, and change the Search dropdown from All to Up. To get a count, click the Find In button and click Main Document (or one of the other choices if available). The count appears in the dialog.

d. I think I’ve noticed that Find does not work 100% of the time. True?

That's not my experience, with one exception: If you use a wildcard expression when the "Use wildcards" box is not checked, or you use a non-wildcard expression when the box is checked, the search probably won't find anything.

e. The lines of text differ in length between Draft and Print views. This is very inconvenient because Print view shows the final layout but repaginating is very slow.

The original purpose of Draft view in early versions of Word was to minimize the load on the slow CPUs of the time (8086 and 80286 processors). Later, it morphed to a view that minimizes the temptation to fiddle with formatting when you're supposed to be paying attention to wording and organization. Neither of those things has anything to do with line breaks.

When you switch to Page Layout view, it's supposed to be What You See Is What You Get. Almost any reasonably modern processor should be able to keep up with repagination in real time, although those complex tables you mentioned might slow it down -- especially if they're damaged in some way. 

f. Why does repaginating have to happen all the time in Print view even when I make a change that can’t affect it? Very annoying.

Print Layout view repaginates whenever you aren't actively editing. It has done that in every version of Word, because it's trying to be WYSIWYG.

g. My book has three levels of organization: Parts, Chapters, and Sections. When I go to update the page numbers for cross references or TOCs, doing it at the Part level does not work. It keeps asking whether I want to update everything or just the page numbers. Doing a Chapter or Section is OK.

I don't know what you mean by "Part level" -- and neither does Word. The largest functional grouping in Word is the document, and the next largest is the section. How are you defining your Parts, and more importantly, how are you trying to get Word to understand them?

h. I thought that the entries in a TOC were hyperlinked, so that if you click on one it goes there. Mine don’t do that.

If you use one of the "Automatic" tables on the Table of Contents button, the entries should be hyperlinked. You do have to click somewhere inside the content control that contains the TOC before the tooltips will appear, and by default you have to hold Ctrl while clicking to make the jump. (To change that, go to Options > Advanced and uncheck "Use Ctrl+Click to follow hyperlink". Note that this affects all hyperlinks in all documents on your computer.)

If you really don't have hyperlinked entries, press Alt+F9 to display field codes. In the code of the TOC field, add the \h switch (documented here) and then press F9 and choose to update the whole table.

i. At seemingly random times, when I click Home > Paragraph > Numbering, Word hangs up for as much as ten minutes! Any ideas?

Nope. But if you're numbering headings (rather than numbered lists), avoid the Numbering button like the plague. Instead set up a Multilevel List numbering scheme according to this procedure. Anything else is asking for trouble.

j. Why are the Quick Styles not in a sensible order?

The snarky answer is that it is sensible -- to someone. The real answer is that there are many sensible orders, depending on what you're doing and how you prefer to work. You can define your own order. Press Ctrl+Alt+Shift+S to open the Styles pane, and click the Manage Styles button at the bottom. Go to the Recommend tab of the dialog. In turn, click each style you want to see on the Quick Styles gallery; if it's gray, click the Show button; and click the Assign Value button and give it a value. The lowest values appear first on the gallery, and higher ones farther to the right and/or down to the next row.

k. Is there a way to find out what styles are actually used in my document? It would be nice to delete all those that are not used, in one quick step.

Not really. For one thing, you can't delete any of the built-in styles -- Word just won't allow that to happen. You can delete custom styles, either those defined in the document itself or those defined in the base template. If there is any text formatted with a style that you try to delete, you'll be warned; if you continue, that text will be formatted with Normal style.

You can affect which styles are shown in the Styles pane, if you care. On the Styles pane, click the Options button. The "Select styles to show" dropdown claims to let you choose "All styles" (but not really all; only Paragraph, Character, and Linked), "In use" (but that shows some styles that aren't assigned to any text), "In current document" (but this shows the same list as "In use"), or "Recommended" (according to the settings on the Recommend tab of the Manage Styles dialog).

l. Is there an easy way to remove lots of the styles I never use? Deleting one at a time  is  very  slow.

If these are custom styles rather than built-in styles, then yes, you can write a macro to do it. The gist of it is that, for each custom style, the macro does a Find. If no text with that style is found, then the macro deletes the style. If you ask Google, you'll probably find that someone has posted such a macro.

m. Are any of these things improved in Office 2013? If not, why buy it?

If these are your only criteria for whether to buy Office 2013, then you won't find any of them are different in Office 2013. The major focus in 2013 is on integration with the Cloud (particularly OneDrive) and on collaboration with co-workers. There are some very nice new features, but none of them are in the areas you asked about.