Kathy, that’s a great workaround! So then you make the 2nd row in the table the heading for the first page? (Because when you turn no the “skip first” option, that first row disappears on the first page.) I’m embarrassed to say I never thought of that.

Erica,
I suggest:
First, taking a walk or perhaps a bike ride. That will help InDesign cool down enough to work properly.
Next, rebuild your preferences.
Finally, talk more kindly to InDesign. Consider bringing it a gift of flowers (or, in your case, a tumbleweed).

Let me know if that works.

Just to be sure, you are using the final released version of ID, right? (Build 72) I know there were a bunch of bugs with this in prerelease (we’re not supposed to talk about prerelease in public, but… well, there were). The big difference between graphic cells and text cells in CC 2015 is that you need to use the Selection tool to click on images in graphic cells (vs. Type tool for text cells).

I have no problems currently with selecting the right thing at the right time with the right tool.

In the Hyperlinks panel flyout menu you can turn off Auto Update URL Status. (Not sure which version of ID CC they added that feature in.)

So not all paragraphs are tagged? So it might look like:
[A]first paragraph
second paragraph
third paragraph
[B]fourth paragraph

Is that correct? in that case you would search in the GREP tab for:
(?s)^\[A\](.+?)(?=\[)
and then apply the paragraph style A
That grep means “apply this to more than one paragraph, then starting at the beginning of the paragraph, search for [A] followed by any text up to, but not including, another [”

Do you need to change from facing pages to single pages often? That is very rare for most people.
When you turn off Facing Pages, your document should reshuffle. You should not need to delete the odd number pages. It should just work. Does for me. Maybe you have Allow Document Pages to Shuffle disabled?