An internal mass driver engine uses electrical power to accelerate reaction mass in a mass driver and to accelerate a spacecraft that way. Some designs assume relatively large exhaust particles (dust or grains) at relatively low velocity (in the double or single digit kilometers per second).
Would the use of such an engine in relatively congested space (including LEO, GEO, and in the future the Lagrange Points and lunar orbit) be a significant danger to the infrastructure?
relatively low velocity (in the double or single digit kilometers per second).
The distinction is important.
In general, if your exhaust velocity $v_e$ is greater than the local escape velocity $v_{esc}$ minus your current orbital velocity $v_o$, your exhaust might escape the local gravitational sphere of influence. If $v_e > v_{esc} + v_o$ then your exhaust will escape the local gravitational SoI, unless it hits something first.
Orbiting at the distance of the moon, $v_{esc} \approx 1.4 \pu{km/s}$ and $v_o \approx 1 \pu{km/s}$ so if $v_e > 2.4 \pu{km/s}$ then it'll probably be shooting off into interplanetary space, at least. It would be surprising to have an exhaust velocity of less than that, because the specific impulse of your engine would be rather poor, and there are probably better means of propulsion both in terms of efficiency and not polluting the neighbourhood.
If $v_e \approx 10 \pu{km/s}$, then your exhaust will be on an escape trajectory if your orbital radius is at least ~23000 km (which is lower than geosynchronous). Using a grit-cannon at lower altitudes is probably undesirable, given that space starts getting crowded down there, but clearly a double-digit km/s exhaust velocity will not generate fresh space junk around Earth.
Would a direct hit with the exhaust endanger space infrastructure?
Well, yes, obviously. However, in general you'll be pointing your big engines either tangentially to your orbit (for prograde/retrograde burns) or perpendicular to your orbital plane (for plane change manoevers) and as such the exhaust plume will generally be aimed away from what you're orbiting, which means it'll be flying through less busy space, meaning you don't have to worry so much about shooting someone
There are some exceptions, such as being in a lowish, boring orbit in the equatorial plane, in which case some of your thrust could pass through geostationary orbits, so as soon as you're closer than GEO you probably want to be very careful about using your grit-cannon. Other exceptions include thrusting towards the Earth from a Lunar orbit.
would there be a practical risk that exhaust particles exceed escape velocity of the planet and come back on a return orbit around the sun, decades or centuries later?
If you're operating as far out as the Moon, or an Earth-Sun Lagrangian point, then it is almost guaranteed that your exhaust will escape into a heliocentric orbit. If it is at least 12 km/s it might escape into interstellar space, but in order to guarantee that escape it would need to be going a good 72 km/s and that looks a lot more like serious nuclear rocketry than a simple mass driver, to me. It seems likely, then, that most of the exhaust will hang around, to some degree.
Is it likely to be a problem though? Well, space, as the good book says, is big. Very big. Low Earth Orbit is comparatively snug... there's not very much of it, and stuff there has a low orbital period and so there's lots of chances for things to hit you. Things in an Earthlike heliocentric orbit, on the other hand, get at most 1 chance to hit you every 6 months (as opposed to 45 minutes for LEO), and in general periods will be much, much longer.
Given a year or more to expand, even a tightly collimated exhaust beam is going to be spreading right out into a very diffuse cloud so even if you did hit it, you're unlikely to hit more than a very small proportion of the exhaust. Depending on the size of the exhaust particles, you may find that the Yarkovsky or Poynting-Robertson effects will tend to sweep them in towards the Sun, making them someone else's problem over longer timescales.
You talk of dust and grit, and that sort of stuff is already the sort of thing that spacecraft need to be concerned about... we get regularly peppered with cometary debris in significant quantities... far more than you might reasonably expect to produce by flying a bunch of mass drivers about. A spacefaring civilization of the sort that will be producing enough mass driver exhaust to become a realistic problem will have had enough experience and expertise to build appropriate shielding to the point where it seems unlikely to be anything more than an irritation. Maybe they'll have moved to a better propulsion system, too.
I will have a quick go at a reply, and maybe others can improve on this.
This is not something you would do in LEO, though people have considered using dead satellites as reaction mass. If they do, I hope they atomise the debris, but I imagine they know their job and are well aware of Kessler Syndrome. Any extra debris is bad, but several tons of space dust fall to Earth each day and we live with that.
Escape velocity from the Moon is 2.4 Km/sec. If you are out beyond the moon, and your exhaust velocities are greater than this, anything you emit will probably keep going into solar orbit. That is large, and the chance of getting anything back from there is pretty small. If there are other craft nearby, then a polite spaceman always thinks of others when plotting their courses, and keep their jets pointed safely away from others. A less neighbourly sort might use their propulsion system as a weapon.
If you are out at lunar distances and your jet has a spread of a degree, then this would be 6500 Km wide at Earth, which is about the Earth's radius. I imagine you might avoid any burn in this direction in case a larger object got caught up in the jet. However, other than at lift-off, we rarely fly directly away from Earth.
Oxygen will be produced in vastly greater quantities than you have any other use for, being a byproduct of refining most metals and other elements, and liquid or solid oxygen makes a plausible propellant for mass drivers.
Oxygen is of course only stable in liquid or solid form under pressure or at extremely low temperatures, and will not survive exposure to sunlight for very long. In the cislunar environment, it will likely evaporate in seconds...at "double or single digit kilometers per second", perhaps within double or triple digit kilometers, depending on how it's dispersed. The resulting cloud of gas will rapidly expand to harmless densities.
