For starters, in terms of viewing the data, can you check the Coordinate system set in the Table of Contents in ArcMap to see if it is what is expected? (Right-click on Layers in the Table of Contents, then click on the Coordinate System tab). The Table of Contents inherits the Coordinate System of the first layer loaded into it, so make sure it is using the one you expect. Also, check the coordinate system of the DEM to see if that is what is expected. It is possible one or more of the layers you are using do not have an specifically-assigned coordinate system, so are "free floating" and instead rely on the underlying Table of Contents coordinate system to align.
If coordinate system is correct in each case, there are other possibilities that come to mind:
Chris Donohue, GISP
Try adding the attached shapefile (extract from the 7zip file) first to your map, then add the DEM. This will tell ArcMap that the geographic coordinate system is supposed to have a longitude range of 0-360. If it doesn't work, and it may not, you may have to do some adjustments like use the define projection tool to update the shapefile's coordinate system to use the DEM's.
Adding your .shp first solved the longitude range problem! Could you explain me what did you do? haha
Also, about my second problem, now when add the xy data with no coordinate system the data seems to plot correctly, but when I set a coordinate system I get my old problem( the xy data doesn't match the DEM), I don't know why. haha
Also, when I add you .shp, the pixel of the DEM changes its size, so my measurements become incorrect. Do you have any ideia what could be cousing this?
But any way, many thanks . I think you already helped me a lot.
We can't get to the data due to the US government shut-down. Can you please post the extents of the DEM and the xy data--or just sample coordinates of the xy data if you can't get the full extent. What coordinate system is listed for the DEM?