i think qgis might have the ability to do everything you require, however the learning curve is somewhat steep.

it allows you to import data from various maps, including openstreetmap, NASA and many more.

i believe there are free/open source topographic layers that can be imported or ways to add specific data.

it can draw layers, lines and shapes on top of each other with varying translucency and colors.

it can show non-mercator map projections such as stereographic, othrographic or even more obscure ones like the waterman butterfly or some of the ones from the list at the bottom of this page: http://www.quadibloc.com/maps/mapint.htm

if you are doing this for a fantasy world map and not earth, it might add even more difficulty but i've read people on forums claim they could do it, using another program with qgis and on windows only. i don't recall much else since the windows requirement was a block for me. it's probably possible to create the shapefile from scratch.

it has the ability to customize aspects of maps and mapped datum in many more ways that i am incapable of properly explaining, describing, using or understanding. i also have cognitive/developmental disorders, so it might be easier for others, however for me, it's a map creation program i get lost trying to use.