The Androidplot docs have a section about enabling pan & zoom.
For example, you could enable horizontal pan/zoom:
PanZoom.attach(plot, PanZoom.Pan.HORIZONTAL, PanZoom.Zoom.STRETCH_HORIZONTAL);
As far as setting the limits goes, it helps to remember that internally Androidplot is treating all values as numbers. Without seeing more code I can only assume that you are actually using epoch time long values on the x axis. Based on that assumption you can do this:
Date minTime = new Date(...) // earliest date to display
Date maxTime = new Date(...) // latest date to display
plot.getOuterLimits().set(minTime.getTime(), maxTime.getTime(), yourMinY, yourMaxY);