I don't have time for a full response right now, but suffice it to say the answers are rather complex. The wiki is right, but it's also misleading to some extent. It really boils down to how you play the game. If the game is vastly too easy at the start, its unlikely to get that much harder. That said, the first hour (or two, depending on how methodical you are) usually boil down to a land grab that is not particularly difficult (in a sense of your being about to lose or anything), but which has far-reaching implications for the later game, hence still the need for strategy and intelligence all the way through.
In general, the likelihood of your losing to the AI goes up throughout the entire game, depending -- again -- on how you play. If you manage to turtle yourself and just hide most of your planets behind some bottleneck while you do some spot raiding, then that might not hold quite as true. Or if you throw caution to the wind and just try to capture stuff constantly while not paying enough attention to protecting your flanks, there will come a tipping point past which the AI brutally murders you.
In many respects, the AI Progress is pretty much a self-balancing thing, so that the difficulty adapts to how you play as you go. That said, it's not going to compensate for something that is orders of magnitude too easy or hard. I'd suggest sticking with diff 8 and seeing how it goes.
As to the question of if your computer can handle 120 planets, that's similarly hard to answer -- it depends on how you play. Are you planning on trying to capture all 120 planets in an 80-hour odyssey that will lead to 200k+ ship counts? Then your computer will be pretty hard-pressed, but has a chance of holding up at about half the normal framerate by the end. If you're planning on playing more or less a "normal" game and taking 20-40 of those planets in 13-25 hours or so, you'll probably be just fine on the framerate, or at any rate any dips you have wouldn't be related solely to being on such a huge map.
My guess is that you're fine on both points. Trying to balance the difficulty too finely is rather fruitless, as even the map itself can exert such a huge variance on it. Generally I don't feel threatened myself on diff 7 for the first 8ish hours of a game; but I've lost the last 5 out of 6 games I've played. Not being immediately threatened is very different from there being no challenge, by the way. You're setting up very long term positioning and strategies, and so is the AI. You have to keep an eye on what you're doing and what they are, or else you'll put yourself in a bad position down the line. On diff 8 I'd be surprised if you didn't have a fun game with a good amount of challenge, if not too much by the end. If you were playing on diff 1, that would be a different story, which is what the wiki was referring to.