comprehensive explanation of watch behavior

If you search the Support documents, you'll find couple of them explaining some of your questions. There are two examples here:

• Why Does My Garmin Watch Not Display My Exact Running Pace? 
• What is Pacing?

When searching, better specify your watch model, since the answers may vary depending on the device you use.

As for the alerts "In desired zone!" - that sounds to me more as if you enabled also the HR or HR Zone alert. At least myself, I get these alerts exactly when using HR Zone alerts on Instinct 2. 

... BTW, unlike what is stated in the first document about rounding the current pace to the nearest 5 seconds, after the last firmware update (v8.10), I now get exact pace values. With earlier firmware versions it was true, though. At least, at audio prompts. I am no more sure how it was directly on the screen.

You get a sound when you're outside the zone (too high or too low)  and again when you're inside the zone (if I recall it right - will check today :-) ) 

I appreciate these specific insights, but what I really want to know is if there is some reference material - preferably provided by Garmin - that explains all of this comprehensively.

That's exactly what I would expect, but I got an alert and when I looked at the watch, it showed a pace reading that was within the zone. I would love to find an explanation of when and why the watch gives these alerts.

I just looked in the downloadable manual and at least in the German version the Alarm settings for pace, HR are described quite detailed. Have you looked in the English manual? 

I have, but am happy to look again. For example, I find this: https://www8.garmin.com/manuals/webhelp/GUID-31D23DBB-57C2-4DF7-A0C9-8D1A00AB4BE7/EN-US/GUID-E9B4413D-28EB-4054-8622-5CCD3F4571D2.html

This tells me how to set an alert for pace, heart rate, cadence, etc. The issue is, I am getting alerts that then show a pace that is within the range...

I set the pace range: 9:00 - 10:00 min/mile

Watch beeps. I look at it and the screen says "Pace 9:08"

Some seconds later, the watch beeps again. I look at it and it says "In designated range!" (Or "desired range," I forget.)

So, what's going on? Is the watch alerting when I get "close" to a range limit? Is it simply showing the pace over the last X period of time or Y distance - unrelated to the range? The point is, I don't know why the watch is beeping/alerting and can find no resource to explain the watch's behavior. And, this is not the only aspect I am curious about. There are maybe a dozen others.

The first time I did a 40:00 run, the watch started beeping at the end, so I stopped running. I looked at the watch and saw there were 5 seconds left... so it was beeping 5 seconds early to warn me of the approaching end. Now I know. No big deal. But is there somewhere that explains that the watch will give me a 5-second warning? (This is one reason I think maybe the pace alert is giving me a "you're getting close to your range limit" warning.)

As another example, I figured out that the watch beeps at each mile interval and shows the pace for that mile. There's a mile count number in the GPS circle and a pace readout. This is pretty intuitive, so easy to guess. But it's POSSIBLE that at each mile interval, it might show you the average pace for the whole run rather than just for the latest mile. If you didn't KNOW, how would you find out? I want a reference document that says "The watch will beep at each mile interval and show you the miles in the top-right circle and the pace for the most recent mile."

I cannot believe this document doesn't exist, so thought I must be missing something.

7633900 said:

Watch beeps. I look at it and the screen says "Pace 9:08"

Are you sure you did not activate the HR alarm, and do not confuse it for the pace alarm, as I already suggested earlier?

This is what my workout looks like (I have adjusted the pace target since I started this thread, but the same thing happened to me this morning... alerts and then pace within target range). But also, if it were going by a HR alert, why would the watch display the pace and not the heart rate?

7633900 said:

This is what my workout looks like

HR alerts are not a part of the workout. You can enable/disable them in the settings of the concerned activity. They are independent on the workout pace alerts.