Welcome to the forums! And, hope you enjoy AI War and stick around if you do take the plunge.
To your questions:
1. Yes, you get a steam key as well as a regular key. If you buy it elsewhere, you can also register that other key on Steam (Activate key on Steam, down at the bottom) to have it on Steam. Basically, we tried to make it as easy as possible.
2. Version 2.0 was a particularly major milestone, hence the notes on there about that. The current official version of the game is actually 3.060. All version updates are free for all existing customers of the game, and are basically what constitute our general maintenance as well as our "free DLC" updates. The current beta version is 3.084, and that is also free for anyone to use if they have the base game (or the demo of the base game, in both cases, as well). The expansion code is all part of the one single executable that we have, so that is updated right along with anything else. When you buy the expansion you are basically buying an unlock key and a content download -- we only have one executable, period, for the base game, the demo, and any and all expansions that will ever come. That keeps things super compatible and simple for users (and us), and makes it so that interface improvements, bugfixes etc, are always for everyone, and not just people on the latest expansion. You only need an expansion if you want the added content it contains, not if you want to be assured of being up to date on fixes, etc.
3. No worries on the beta updates, those work perfectly well with Steam in our case. The in-game updater does just fine. Same with Impulse or any other vendor. We don't use any DRM even with Steam, and so that again makes things simpler.
4. Usually Steam gets the official updates within a few business days of them coming out. But if you're already up to date on the latest betas, generally there is little difference between the last beta before an official, and the official version itself.
5. I already answered this one above, but no you don't need Zenith for beta updates, or for any other purposes aside from if you want the content in Zenith. We don't like holding people hostage for updates unless they buy our expansions, in essence.
6. Yes, AI War very much benefits from a GPU, but not in the fashion you are thinking. The game can have a ton of ships onscreen at once, and a solid GPU will make a difference in those cases. It won't exactly speed up the simulation per se, but if your CPU otherwise would have been carrying some of the graphics load (thus making less CPU time for the simulation), then the presence of the GPU will free up more CPU to be used on the GPU. There are a number of reasons why multiple cores, or CPU-based stuff, can't really be used for the simulation proper (it's basically a problem that no one has ever solved for a deterministic multiplayer lockstep simulation before, to my knowledge -- there are some other posts about that on the forums if you search). At any rate, the GPU specifically tends to be quite busy enough with AI War anyway, depending on the scale of your games, so that wouldn't be a solution for us.
7. I do know of some players that are playing on netbooks, but your mileage will really vary based on the netbook (it would have to be a really recent netbook to stand any chance, from what I recall). One other thing to watch out for is the screen resolution, as that can make a couple of AI War menus hang off the top/bottom of the screen. That's annoying, but the game is still playable (the minimum supported resolution of the game is 1024x768, which is standard on desktops but not netbooks -- but, we do allow players to set it much smaller than that, since some like to run it on a netbook despite the few issues with the menus).
You'll find that with a single core it will run noticeably worse unless you are a client in multiplayer, as you say. But, depending on the simulation you are running, it might be just fine. There are two things working against you, simulation-wise: time and map size. The longer you play a game, the more ships the AI will build up on its planets. If you play an 80 planet map and win in the expected 9-13 hours or so, then you'll probably wind up with only around 60k units in the game (probably more than a netbook can handle still, though). If you play that same map for 30+ hours, you're probably looking at over 100k units in that game, which starts choking even midrange desktop computers (apparently the really high end desktops laugh at even 200k units). Each campaign really wasn't designed to last more than 15-20 hours, but some players take it north of 60 hours, and that causes more load based on the increased number of ships. The larger the map, the more that is exacerbated. There is a finite limit of around 4.4k AI ships per planets it holds, so given infinite time you eventually max out how many ships the AI will have (if the AI had 110 planets, that would be 484,000 ships, for instance; versus if the AI has 6 planets that would only be 26,400 ships at absolute most).
10 planet maps and 20 planet maps have a distinctly different feel from the larger maps. In some respects they can actually be quite harder. I would generally recommend playing in the 40-80 planet range, but that requires more CPU power. The demo is the full game, just not yet unlocked, so you can play the first 3 hours of a campaign and see how it does. Like I mentioned, though, the load-based-on-time will only get higher as you go. If you want to do some load tests, try doing multi-planet starts, larger maps, or overpowered AIs (perhaps with yourself at a large handicap so you don't just die immediately). That can simulate normal end-game situations much better.
I do know of some players who are 80+ hours into a 100 planet map, and the host is on a 1.6Ghz dual core. I also know they are playing at around 1/3 speed at this late stage, but that doesn't seem to bother them all that much. It's one of those cases where they are really pushing the limits of the gametime in general, and doing so on the bare minimum system requirements, so of course the end result is not ideal. Personally I've played 15-hour 80-planet games with a 1.8 Ghz single core desktop (older P4, no less) that ran as the client in a 2-player game with no lag. But your mileage may vary based on the type of processor architecture you have, other factors like RAM/HDD speed, bus speed in general, and so on. Not to mention what sort of maps, etc, you play. It is very hard to predict performance on a specific machine since "1.6Ghz" can mean so many different things. If it's a newer processor architecture, it will likely do pretty well, if not stellar, versus if it's something from 8 years ago it probably has no hope. That's the problem when writing system requirements, is that there are no overall objective measurements!
Hope that helps!