The control arms are simply the lever arms that attach the rear axle to the body of the car. The lower control arms allow the axle to move up and down; the upper control arm allows it to move up and down and also prevents it from rotating due to the torque from the engine/driveshaft. The bushings at each attachment point absorb some of the noise, vibration, and harshness ("NVH") from the axle; while at the same time preventing excessive movement of the attachment points. If those bushings are worn out, it can introduce excess play at those attachment points; but you are only talking about maybe 1/4" or so; might be noticeable if they are really bad but generally so small that you probably won't feel it.
Like I mentioned earlier, the reason people replace the lower control arms is usually to stop "wheel hop" ; which happens because the factory arms are relatively flexible and have soft rubber bushings, so on a hard launch they bend, then unbend, then bend again, very rapidly; and you get this pounding banging affect which is called "wheel hop." The upper control arms are sometimes replaced with an adjustable arm, to correct or fine-tune the pinion angle. There are a few other subtleties to this but they mainly apply to road course cars. Another reason to replace them, is if the bushings are shot.
Control arms generally cannot be "too stiff" because they have a rotating joint at both ends. The trade-off with the bushings is that the harder bushings in the aftermarket control arms transmit more NVH than the soft factory ones. If the bushings in the upper control are are so hard that they do not allow the axle to rotate when one wheel hits a bump, that can cause binding . . . but usually not an issue. If the bushings bind up they could prevent the arms from moving up and down like they should, but I think that would be extremely rare.
I am not sure of the factory spring rates, but they are probably available out on the interwebs somewhere. Be aware that progressive rates can be deceiving; the initial rate is much lower than the rate after some compression. 165 and 160 sounds fairly low to me, but I am not sure. Lowering the car reduces the travel available for the suspension, and combined with soft springs, that could cause the suspension to bottom out more than it should. You would feel this as a hard bump/thud over big bumps.
Standard disclaimer: "that's how I understand it and I'm explaining to the best of my ability."
You are welcome to get a "second opinion" or course, but those are the basics and I'll be interested to see if we hear much different.