Zbrush doesn't smooth between polygons, it's Flat Shaded all the way. Models only appear smooth with the polygons get so dense and small on the screen that your eyes can no longer notice the subtle difference in planes.
You can subdivide (normally or dynamically) a few levels to make the model appear smoother.
Yep, smoothing groups aren't a thing in zBrush (or most applications really). You could use auto crease and subd that way, or sub-d a bunch in max using smoothing groups, and import that (heavier) file into zbrush.
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You can subdivide (normally or dynamically) a few levels to make the model appear smoother.