To answer your Questions:

1 & 2: A Lattice is a deformer and was designed for use with animation. But more and more it is being used for modeling.

Once you create your lattice on the chosen object then object can be moved in and out of it and you will see the geometry deform as its pulled thru. Any other object should also be effected by it.

Really I'm not best to explain it, but use the link below and it will send you to the Digital Tutors Website for a free tutorial on Lattices. This will give you the overview you need.

Lattices 101

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