I hope you can help me fix it.
This is called shadow terminator artifact and happens with some render engines on low poly meshes. It is a limitation that Cycles has, devs know about it.
The solution is to increase the polygon count.
The black on the silhouette is another kind of artifacts you might encounter called rejection sampling - also does go away with polycount.
You can change also the shading method. Your whole surface is set to smooth - it is interpolating the surface normals making shadows where there probably shouldn't be. You may want to turn on Auto-smooth or set some sharp edges: