The laser terminal would, almost certainly, be on an orbiter, it would receive data from the rover via Radio communication (this could be at a fairly high rate, since the orbiter would be so close to the rover, and then the orbiter would relay the data to Earth via laser.

Remember, mars is dusty, and all that dust would greatly compromise a laser transmitter on the surface... so forget the 'almost certainly' above... it would CERTAINLY be on an orbiter.

The width of the beam would depend on many factors... how collimated the beam is limited by the diffraction limit of the transmitting telescope. Larger transmitter telescope, the narrower the beam, the shorter the wavelength the narrower the beam... the beam divergence would likely be on the order of 10 micro-radians, or 2 arcsec... perhaps as small as 2-3 microrad, but let's assume 10.

I think at mars' closest approach to earth this gives you ~560 km spot on earth, but its late and I am doing this on my phone...

The laser transmitted in the Lunar lasercom demonstration had a footprint on the earth of ~ 6 kilometers in diameter. For comparison an RF signal would cover most of the continental US.

One of the most difficult problems in lasercom is how to aim something that precisely.. and you have to aim at where your target WILL be when your laser signal gets there... NOT WHERE YOU SEE IT.

The more collimated the beam is, the more power arrives at your receiver, BUT the more collimated it is, the more precise your aim has to be...

The data rate would vary widely based on distance, the closest Mars gets to us is ~56 million km, and the furthest is 400million km... a factor of 7.14 further, the data rate will vary with the received intensity, which goes as the distance squared. So the data rate will be ~ 50 times higher at its closest than at its furthest... but it gets worse than that, at it's furthest, your receiver on Earth will be pointing close to the sun, this means MUCH more noise, you will have to pick the few signal photons you receive out of all the background sunlight...

The canceled mars lasercom demo was going to use Palomar telescope as a receiver...

More later...