You have definitely been doing your homework on CNC! There are a number of logical if incorrect assumptions newbs invariably make when looking at all this stuff for the first time though. A lot of it is pretty confusing. Hope this helps and doesn't make it more confusing!
First off let me say that ballscrews are nice for a number of reasons, but accuracy isn't necessarily one of them. Ballscrews can be less accurate than an acme screw or have higher backlash. I favor ballscrews usually, but one isn't always inherently superior over the other, they both have their place. In your context, ballscrews might be nicer but not a big issue to worry about much either way.
The stepper versus servo issue is a complex one, but it is not cut and dried. For small mills doing this sort of work steppers and servos have such little to separate them sometimes it is almost academic. Different story on a Bridgeport sized machine, but for this it's almost a wash. Steppers can even actually have the advantage, and in your case probably do. "Lost steps" is more a classic sales bogeyman than an actual problem in your context. So is the argument that there is a reason all the "big mills" do it that way, and so by extension paint steppers as some sort of half-measure - the reason the big mills use servos has more to do with the fact they are well, big. Notice that most small high-accuracy devices use steppers regardless of cost. Scale matters here.
The difference between mill and router usually is more a generalization about their intended function than anything. Routers just generally run toward larger envelopes, faster running, lighter materials, and to hold less tolerance than a mill. Routers often are of the gantry type and mills usually aren't, but that isn't even always a good measure to make the distinction.
Linear ball races are a form of linear bearing, and don't have anything to do with ballscrews. In your example the IMS axis actually uses a traditional screw, but runs back and forth using a simple ball-bearing containing tube on the linear shafting, as opposed to a traditional solid bronze bushing.
Finally, resolution is just as much of a joke as you suspect. It is simply the distance traveled for each incremental step. Take the screw pitch times the microstep increment and you have it. Carve a thread onto a stick with a pocketknife while drunk, and as long as you just rotate it a really small amount each step, you get resolution in the millionths! As you can tell, it doesn't mean jack, but it sure sounds impressive. Dealers often use resolution numbers when the real numbers that count - accuracy and repeatability - don't come out looking quite so hot....
Hope this helps. A lot of the answers might be different if you were looking larger, higher budget, production environment, etc. but for what you want there isn't any real cost/benefit for going fancy. The differences are minor at best within the envelope, materials, and work you need to accomplish.