1) When a ship or building completes, there's a popup square on the right side of the screen. The ships are blue boxes, whereas the improvements are green-though the improvement boxes show dependent on what your setting for them is; you can set it so that they don't show if the planet is still building something. Right clicking on the blue ship box will launch the ship while taking you to it, while left clicking on it will simply take you to the ship in question.
There have been issues with the ship build notification boxes not showing up reliably late game in very large galaxies with lots of ships and planets, but this is generally not something your average player runs into.
There is also an event log in the civilization manager window, although I'm not positive ships show up there, despite the fact that they're theoretically supposed to.
2) You can make a faster freighter, but it only cuts the time that it takes for it to start the trade route. After it starts it, it's set to a speed of 1 (maybe this is 2 in TA, since TA's base speed is 2, but I haven't checked), ignoring all engines and bonuses. So there's really not much point. Trade routes do factor in how long they've been in existence for their income function (apparently) as well, though, so you could theoretically make as much out of a much shorter trade route smply by having it go back and forth much more often.
The money is paid per turn, but will fluctuate up and down dependent on where in the route the freighter is.
You can send as many freighters from one planet to another planet as you like, provided you don't exceed your maximum number of trade routes, which has a global cap at 12 if memory serves, with all trade research completed.
I dislike the trade aspect of the game, personally-primarily because, comparative to taxation, its impact on my economy is very minimal.
3) In the Upgrade window, by clicking Upgrade on a single ship, you have a check box in the upper left hand corner to Upgrade All Ships of This Class. That's the closest you'll get.
4) The Drengin in particular are normally fairly aggressive (ignoring the expanding bug a number of people have encountered in the latest TA), and in general any evil race (Korx, Korath, Yor) will be more aggressive than a good or neutral race as well. At Tough or Crippling you can expect to have to start either defending yourself or striking preemptively (with the latter being preferred), but that varies from player to player.
Tough is considered the baseline difficulty, at which point the AI gets no bonuses or penalties and the player gets no bonuses (the player never gets any penalties, strictly speaking). Sub-normal difficulties confer a slight economic bonus on the player and run the AI at a percentage of its economic output, so while they're helpful to learn the game, they're not so great for learning strategies.
5) Yes. The problem that you've noticed here is that morale is depreciated by population on both an additive and a multiplicative basis.
I don't have a 9B number because I didn't play the Yor for this test.
Pop: malus, multiplier
8B: -18%, 0.82
10B: -25%, 0.75
11B: -28%, 0.72
12B: -32%, 0.68
13B: -36%, 0.64
14B: -40%, 0.60
15B: -44%, 0.56
16B: -48%, 0.52
17B: -52%, 0.48
18B: -57%, 0.43
19B: -61%, 0.39
20B: -66%, 0.34
21B: -70%, 0.30
22B: -75%, 0.25
23B: -80%, 0.20
24B: -85%, 0.15
25B: -90%, 0.10
So going from 10B to 14B I lose 15% additive and rather than having 75% of my morale structures/racial points having an effect, I have only 60%, or 80% of that total, having an effect. So to have 100% approval at 14B pop, I'd need 140% approval at 10B pop (100 / 0.8 + 15), and as you can see, the higher you go, the worse it gets. Most people will stop their planets somewhere between 12B (DA)/14B (TA) to 18B (DA)/20B (TA), which is basically one or two "full" farms. Technically you get access to a +7mt farm using most of the TA trees, but it's better to just use the +6mt farm.
So if you weren't so concerned with filling up your planets with farms and morale structures, you'd probably be able to run a high enough tax rate to finance filling every tile.

6) The demo only allows you 3 game years-approximately 150 turns. I can't remember, but I think it was limited in galaxy size as well, so there's a limited amount of resources no matter what. Without being more specific I can't really address your research concerns, although even with the additional +50% modifier to weapons/defense techs in TA weapons are much cheaper there than in DL/DA, but I'm going to go out on a limb here and say that your perception of the slow pace of research probably has to do with your population/approval/income problems.
The research buildings themselves start at around 6tp and max out at 18/22 for DL/DA and 16/18 for TA, where the first number is the discovery sphere and the second number is the neutrality learning center (for which you have to choose neutral when researching Xeno Ethics to gain access to). Obviously TA's unique tech trees mess with this balance somewhat, but in general everyone starts around 6 and can reach 16, with the exception of the Drengin at 12, the Torians at 10, and the Iconians who don't have a basic (spammable) building prior to their 10. The interesting part is that as far as I'm aware all civs have access to the neutrality learning centers (18), provided the choose the neutral ethical path upon research of xeno ethics. A couple of the racial trees in TA even provide research bonuses as well.
7) Not sure-I'm fairly positive a changelog is put up with almost every patch, but if you're asking for the entire history of the game, good luck is all I can say. I certainly think it'd be nice to have, but I'm not holding my breath, personally.