Detect Infrared beam projected onto X-Y plane. Save and display coordinates. CMOS sensor?
I think the simplest and cheapest way to get beam width and the coordinates where the beam hits the target is to use a camera.

Get a webcam.  Take it apart, and remove the IR filter.  Reassemble it.

You now have a webcam that can see light and IR.

Aim it at your target, with the camera at a fixed distance  from the target.

When your laser is in operation, you should see a bright spot on your image.

Since the target is a fixed size and the camera distance is fixed, you can figure out calibration numbers such that you can calculate positions in millimeters from the image pixels.

This gets you position information (where is the bright spot?) as well as beam area (count the pixels in the bright spot.)

I think if your target is flat, and you roughen the surface slightly (matte instead of shiny surface) then you would get a slightly wider beam image.

In any case, the beam area and intensity can be used to estimate the distance from the laser to the target.



You'll need to disable autoexposure and shutter speed on the camera if you want to use the brightness to estimate distance.  Those two automatic settings will vary the brightness, and you'd be hard pressed to compensate for that.  

Set the shutter speed and exposure to values that work well in your environment, then calibrate the brightness and beam area against known distances from laser to target.  Then, always use those shutter and exposure settings.

There are commercially available IR cameras, and surveillance cameras that can see IR and visible light.  If the resolution or quality of a (high resolution) webcam isn't good enough, you could move up to better equipment.  But, I think the webcam will do to at least prove the concept before you invest a lot of money.

You may find OpenCV useful in handling your camera images.