Is there any way to turn off randomization of the billboard placement and just rely on single pixels on the control map to place single billboards exactly (corn rows for example)? And is there any way to just have the billboards rotate on the Y axis?
You would have to modify the script for that.
For drawing the grass blades only upwards there is a up vector which the script passes to the shader every frame which is the up vector of the camera. You can modify that to be Vector3.up instead. I think this is done in the SetupShader function of the script.