@bertrand You can determine bad bushings by prying on them when the car is in the air. One of the 2 bushings is very stiff and the other is usually fairly soft. Neither should rattle around. The stiff one should move very little with a prybar and the larger/softer one will move a bit but, again, not very much with a prybar.
Very often, to sell you new bushings, they will just point to cracks in the bushings and declare “replacement time - translation BOAT PAYMENT” when they will last quite a bit longer. What you can see is not the “working” part of the bushing is is just the exposed part.
Ball joints are just about slop in the joint and torn grease boots. If I saw a torn boot and a grease-dry joint underneath, I’d suggest replacement because dry joints greatly accelerate the wear and I don’t know how long its been that way. At 100,000+ miles, why not do the entire arm if the ball joint needs replacing? The bushings aren’t that far behind.
The lower control arm takes every bump and pothole and every acceleration and braking you do. It works very hard. It is tested by the manufacturer by puling and pushing frontwards and backwards at twice the weight of the corner of the car for millions of cycles. It is further tested at 6 times the weight for thousands of cycles. They also drive the car into a curb at 45 degrees at speed just to see that it bends, not breaks. It leads a tough life.