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Hello, Baz,
Yes, as Mike says, you can see sunspots re-emerge, though it's not a given as many are short-lived. The sun rotates relative to the Earth around and about every 25 days. So for nearly a fortnight any given sunspot is out of view. Most sunspots don't last that long.
As far as the positioning of sunspots is concerned they seem to move in an approximately eleven to twelve year cycle (as we see them). During this time they tend to move towards the poles and their frequency decreases. I don't mean individually, just the latitude of their appearance. At this point in time we are at a 'low' sunspot cycle - meaning that there are not many of them. Over the next few years (five to six if predictions hold true) you will see many more sunspots most of which will appear close to the Sun's equator.
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