1. I have never used the OCAD versions of this, but I think this is what you want. Save a second copy of the map file. On this second copy, take any linear object (I typically use a big pink line), and draw the boundaries of the area of map you want to keep. Go to your edit points tool, and select this object. You should now be able to click the "Cut Out" tool which looks like a small section of map surrounded by a pink circle. It is on the right hand side of the toolbar next to the measure tool. Click this button, and presto. The map is cropped to your selection. Delete the linear object you used as the boundary (for me the pink line), and you're done.
2. Moving a linear object. Use either your Edit Points or Edit Lines tools, and select the object you want to move. When you select the object, the points of the object (blue or grey squares or diamonds), the bezier curves (blue circles), and a purple rectangle surrounding object appear. When you hover over this purple rectangle, it should turn yellow. Click, hold and drag the rectangle - this moves your object. This works for linear objects, areas, and if you zoom in far enough, for point objects as well.
Online Source for Mapper Help- Problems, bug fixes, help, etc. https://github.com/OpenOrienteering/mapper/issues
Hope that helps.