It doesn't sound like you need to illuminate the scene with a laser spotlight, it sounds like they will input a small amount of laser light into the crystal film on the glasses. The externally sourced IR photons will combine with the internally generated laser photons and emit a visible frequency photon.
The amount of laser energy pumped into the crystal film will probably be proportional to the amount of energy you want out of your "screen", i.e. brightness
Not at all. For a single photon, sure. But in aggregate many low-energy photons can charge a material to emit fewer high-energy photons. Ex. https://www.newport.com/f/near-infrared-nir-sensor-cards
That would, for instance, allow you to make safety goggles for detecting hot spots. Could be useful for firefighters or factory workers.
The problem with a passive device would be that if you walked past something hot enough your goggles would white out (well, red out), and you might be effectively blind. At least with the passive device you can turn it off briefly so you can see where you're going.
You can't do this with a passive device, because the single visible photon has less total entropy than the three infrared photons. Yes, it satisfies the first law of thermo, but it violates the second.
The incoherent case is the relevant situation when you're talking about passive glasses for viewing a scene in ambient IR light.
Here's one place where this is mentioned:
http://physics.stackexchange.com/questions/98790/what-low-le...
Still looking for an authoritative treatment...
To be fair that's exactly where NVD technology started out https://en.wikipedia.org/wiki/Zielger%C3%A4t_1229