Some of these might be bugs, some of them might be intentional by design...but I figure there's surely people around here who know better than I do! Sorry if any of these are already dead horses...I tried to stay away from stuff like multiplayer.

1 -- I built a terror star next to the Drengin home star system. It sat there mobilizing for 10 weeks, and they didn't lift a finger on the "tough" difficulty. Granted, we weren't at war, but if someone was building a gigantic death ray aimed at my homeworld's star, shouldn't it be considered a "red flag"?
This sound like an AI 'bug'. More like an oversight, though: they should definitely be worried. Brad usually notices these posts, though, and fixes the bugs.
2 -- Is it intentional to have ships "gain" movement by stopping at a friendly planet on the way? Entering and leaving orbit takes no movement, so I can go a total of 5 distance using only 3 movement as long as I go through a planet.
Never heard of this... sounds like a bug, though.
3 -- I was playing the Iconian Refuge, and I chose some evil action on my only occasion for one of those "moral choice" events. Then, when it came time to pick my ethical alignment, my little ticker was sitting as high on the "good" scale as you can go. Aren't your choices supposed to move your alignment?
The ethical alignment is a scale from 99 (pure good) to 0 (pure evil). The Ethical Choices only move a few steps on this scale, so someone like the Iconians, who I'm pretty sure start on 99 on the scale, it would be quite understandable if you didn't even get to neutral.
4 -- Anecdotally, it seems like I don't get any more ethical choices after I choose my ethical alignment. Is that true? And if not, would there be any penalties for the saintly Iconians to make evil choices?
This is true. The Moral Choices are to choose your alignment, basically. (they stop after you choose alignment) Although you get to choose in the end, making Good choices makes it 10,000 bc to become evil.
5 -- Why do ships sometimes have more HP than their maximum, (eg. 37/32)?
Many reasons. It's not really a maximum, just a normal 'full' HP.
6 -- What's the rationale by which ships gain HP? In my current game as the Iconians, I've had medium sized ships gain a few HP by knocking out measly enemy freighters. Yet in games as other races, gaining HP after victories seems rare.
Iconians have huge repair bonuses.
7 -- Is it intentional to have no "buildup" of star dock resources? For example, if I am 50% towards building a 400BC ship, and then I switch to building a 100BC ship, I'll get one 100BC ship, but after that I start from scratch. I would have expected to get two 100BC ships.
I don't know if it's intentional... it could be either way...
8 -- Why a limit of 1 starship per week per planet?
Why not, really? Easier to code, probably.