Just use smooth (as described) to view your model smoothed - always remember to undo it before carrying on modelling.
If you smooth it, delete history and then save it then you'll not be able to go back to the unsmoothed version.
Before duplicating the other half, go to front view, click on a vertice which will overlap, press and hold x (snaps to the grid) and move the left-right move arrow. The vertice will snap to each part of the grid you move the mouse over - move it to the central line. Do this for all the offending vertices then do your usual duplicate command and they should all be sitting nicely without any overlap.
Looks like the model is coming on well - keep it up