There actually isn’t a difference between the two. If you are box squatting to parallel and squatting to parallel your 1rm should be the same. The problem with box squatting is when you sit and rest at the bottom of it. All the force goes to your spine. You should lightly touch and then drive up. I hope that answers your question.
This is not good advice. At all.
The point of doing box squats is to build starting strength, not merely to gauge your depth (this is better accomplished by observation of training partners, videotaping yourself, etc.)
You want to pause on the box, releasing the tension in your hips (but keeping your abs inflated,) then re-tighten and drive up.
Your carryover will depend on a host of factors; most important is how well you use the stretch reflex. If you are good at using the stretch reflex but are weak, box squats will help you a ton. If you are strong but don’t take advantage of the stretch-reflex, you should focus a lot of time on free squatting.
Box squatting may also be more useful for a lifter who uses gear b/c the squat suit stores energy on the decent and provides pop out of the bottom. Building speed off the box will ensure that when you get to the point where the pop out of the bottom is finished, you will have enough speed and momentum to finish the lift.
You are correct in saying that you take away the stretch reflex when you box squat but you are greatly mistaken when you say that the box squat is good for starting strength. If you look at the reearch out there any time you squat you get lower banch and spinal compression. Now the degree to which you get the compression depends on body position.
A recent study said that if you squat and allow your knees to pronate forward slightly your knees will get approximately 28 times more of the compression forces. If you keep your knees aligned your back will get 1000 times more. When you box squat and sit down then you are doing damage to your Lumbar and Cervical area. Over time this could cause problems down the road.
Also if you want to work on your starting strength. Get in a power rack and start in the bottom position Or perform pauses with 60% of your 1RM. It is much safer.
Box squats are not good for starting strength? I disagree. I think that they are one of the best exercises for starting strength in the squat. In my opinion, better than rack or “bottom postion” squats and pause squats.
I disagree with your assertion that they are unsafe too. Any lift can be performed in a safe manner and an unsafe manner.