3ds max has much better usability than the confusing interface of Blender.
1) To manipulate verticies you need to be in vertex mode. Right click on your mesh and hit convert to editable poly (or editable mesh if you want to work with triangles), then in the stack on the right expand "editable poly" and click vertex. Or under "selection" on the right click the 3 red dots which means vertex mode.
Now you can manipulate verticies. If select verticies with the move tool and don't see the dragging arrows, you may have accidentally turned off the gizmo. Hitting 'x' toggles it.
2) I'm not sure what you're asking. Do you mean switch your current tool from move to rotate / scale etc?
3) 3ds max has powerful lighting capabilities. The simplest way is to add a skylight to your scene. On the right sidebar click the create icon (the little mouse with the splash of light), then click the lights icon, and add a skylight to your scene. Then you need to activate advanced lighting. Go to Rendering > Advanced Lighting > Light Tracer. This will activate it by default, and rendering will now show occlusion.
