To understand how Cartographica works with CRS/Projections, the key is to understand the relationship between the "Map Projection" and the "Layer Projection" and the fact that any time the software says "Projection", we are referring to Projection or CRS.
With the CRS naming issue out of the way, the Map Projection is set in the Map menu with Map > Project Map... This setting determines what shows up in the window. No matter what your input data is in any of the layers it is working with, the Map projection determines what is shown visually.
The Layer Projection is a declaration of the Projection/CRS for the data in each layer. Generally, this comes from the .prj file if you are importing shape files, or from other sources with other file formats. However, if you import a file that does not have any kind of Projection/CRS information associated with it, Cartographica (1.2.2 and later) will put a little triangle in the layer stack to warn you that you need to set one or it will be confused.
We use a lot of heuristics to try and work even when a CRS isn't declared, but they mostly fail except on simple maps.
As for "Reproject data", we take two separate meanings for that. One is what we do internally behind the scenes to change the data for display. That we do automatically and there's nothing you need to do except set the Map projection. If, on the other hand, you want to export data to another device or program that requires the data to be in a different projection, we have a way to do that as well. Note that it is destructive, so you will want to back up the layer before making the change (there is also a warning message in the window). To reproject a single layer (changing both its declared projection and replacing the geometry features with identical features in the new projection) use the Layer > Reproject Layer... menu command.
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