The on-board propellant would be hydrogen, just like an NTR, so we can expect similar specific impulse. However, since the choice of materials for the laser-heated HX is much less limited than the choice of reactor (fission fuel) materials, the achievable specific impulse should be higher than an NTR -- probably in excess of 1000 sec.
Not if the end of the vehicle contained the final focussing optics as a part of the engine bell. You just have to keep the beam focussed on a spot no bigger than two meters across--almost a piece of cake. (O.K., it might be a little hard!)
What I wonder is a, how do you aim that laser beam so it hits only the exhaust, and b, how do you keep the "focussing optics" from melting because of the hot exhaust?
Actually, I was thinking of a different arrangement, where the laser ground station is over a hundred miles down-range from the launch site -- so the incidence angle of the beam on the belly of the SSTO is around 90 degrees, but obviously varying as the craft approaches and departs.
The HX target area on the belly of the SSTO would be considerably larger than either a rocket nozzle, or the diameter of an ICBM. The ABL (AirBorne Laser) aircraft is slated to demonstrate an ICBM intercept in the coming years -- that's a hit from one moving object on another moving object (the ICBM). Presumably this would be considerably easier for a ground-based laser, with a very predictable & larger target.....