If I am reading the question correctly it seems that they can only control existing light, not spontaneously generate light on their own.
This would then come down to how much light is in the immediate area for them to direct. Also this could look really weird depending how they did it, almost like a big shadow or dark spot appearing as they redirect the light in a different direction.
The sun puts out about 1300 Watts/m^2 on Earth. If they can gather the light from a moderate area, say 10 m^2, then they have about 13 kW of power to play with.
They would obviously be more powerful in daylight, or with other light sources around. To supplement this I would recommend that they carry flares or other fast sources of light, I can imagine they could do some really interesting things around say a room full of high power lasers.
Not likely, the photon pressure from the sun is measure in micro Newtons per square meter. So even if they can put a million times the suns photons on a 1 m^2 surface they are only exerting around 1 newton of force (about 1/4 of a pound). This would likely move the object, but it would also unfortunately first incinerate the item with about 1300 Mega Watts of power.
They could potentially focus some of that power to move objects around by creating thermal air expansion (AKA wind) or small fires/explosions to move the items.
This does work, with a bunch of caveats that make it effectively useless as a super power. Currently it only works for individuals atoms or at best molecules by changing the particle momentum. It really only works when the samples are isolate at near vacuum and have already been significantly cooled.
Also it requires lasers to strike both sides of the particles, which really won't work on anything larger than a single particle as all the other atoms get in the way of the lasers. So unless they work at a lab where they are super cooling individual atoms, the power is not going to be of any use.
Totally doable. The Autoignition temperature of many burnable materials are in the 200-300 °C range. As any kid with a magnifying glass knows it only takes the sun light from a small area (the size of a magnifying glass lens) focused into a small area to start a fire. If they can make any illusions larger than a few square centimeters they can start a fire.
- Cut through an object or person:
This is likely going to take some practice and effort, but is probably doable to some extent with the powers you describe. If they can make realistic phantom objects then they can manipulate the color (i.e. frequency of the light), as well as the direction that it is moving. If they have fine enough control of these they can make a light beam equivalent to a laser.
Laser cutters do exist, but they are usually only used to cut thin materials and they use a fair amount of power to do so. The amount of power increases with thickness because there is more material that must be vaporized by the laser. Vaporizing literally means that the material is rapidly melted and boiled into a gas that blows away.
Going back to the first answer it all revolves around how much area they can operate their powers on (basically how big an illusion they can make) you can then use that size to figure out how much solar power they have to play with. Most high power (cutting a few mm thick steel) laser cutters are in the 1-10 kilowatt range, while the low end (effectively wood burners) are in the >1 watt range.
Laser cutters won't however instantly sever limbs or cut through thick objects, they can however cause damage, severe burns, cut though thin items (< 1 cm), or cut through thicker objects if they remain stationary. So you could brand someone, maybe cut off a finger, or give them a really deadly burn, but are not likely to have enough power to sever limbs