On your first question:
ZBrush is not REALLY a substitute for the others. It is used alongside them.
Its the industries choice for sculpting. Normal workflow for high quality assets nowadays is boxmodelling base mesh (Maya, 3DS MAx, Blender, whatever), import base mesh to ZBRush, subdivide, sculpt high poly mesh in ZBrush, retopo and bake high poly to low poly mesh (either in ZBrush or other tools), apply baked normal maps to low poly mesh in Maya / 3DS Max / Blender / whatever, and continue with rigging and animation, if needed.
Blender is always worth mentioning. It is a free open source alternative to Maya / Max. It has its quirks and limitations (does not play nice with meshes imported from other applications, had to switch to Maya LT because of that), but as long as you start in Blender and get to know its UI, it does the job.
Then for Maya you get the LT option that you don't get for 3DS Max to my knowledge. 30€ a month is a very good sub option IMO. Of course money might not be a problem for you (student options might be available), and it seems 3DS Max is better for modelling than Maya (How exactly I haven't found out yet).
On your second question:
Depends what your goal is. If you want to design levels for use in an existing engine, you will have to use the engine editor at some point anyway. You can of course load your exported scene from Maya / Max into the engine editor, but you could also just export the meshes and create the scene in the editor. Personally that is what I do (working in Unity 3D).
If you want to design levels that your own engine / game can load, which might lack an editor, then I cannot say what tool would be better.
If you wanted to know the best tool to create your level assets: any 3D Modeler will do fine. Depending on how the scene will be setup, you might need different output formats (mesh terrain vs heightmap for terrain system in engine), or different quality levels (maybe ZBrush or any other sculpting tool also needs to get invovled for key level props?).
There are some specialized tools that might help you though:
- tools to create and erode natural looking terrain (World Machine for example)
- tools for creating bump / normal maps from diffuse or height maps (Crazy Bump, XNormal or Bitmap2Material come to mind. Xnormal is free software)
How you create and assemble your level assets is a science in itself. It involves 3D Modelling and sculpting, 2D Image editors for Terrain textures and stuff like that, and different plugins and tools to help with assembling everything into a scene (procedural terrain creation and asset placement for example).
