I had a similar problem which I could fix by doubling the standard physics step:
Just scaling up everything might help too.
If understand the working of physics engines right, the reason is the following:
Physics-Engines move all object forward a bit and then check whether collisions happened. A collision happening is defined by two objects intersecting with each other.Thus if you have a small, fast moving object and too big time steps it can happen that your box is just above your ground in one step, which is fine and in the next step it is already beneath, so for the physics engine, no collision happened. If you increase the step frequency, you also increase the likelihood of the physics engine capturing the in-between step when your box is intersecting with your ground. Only if it captures this state, it can prevent it going all the way through it, by moving it back.
Here is a drawing for clarification:
For your second question, this might help: