Sumit,
For the first question, I'm showing a model where displacement is in the -Z and the +Z is help in place with a planar constraint. Is this similar to what you're looking for? Simulate does have the capability to restrict movement in only the -Z direction.
For the second question, try looking at pre-defined measures for displacement over time in the Z direction, as shown below. I'm not sure if this is what you're looking for. It would be nice if you could load an image and problem description of the project.
