Edit: You've edited the question, let me add some to my answer.
If this magical light source inside the fae provides enough energy in the correct wavelengths to get absorb by the plants, there's no reason regular plants couldn't live underground. Vines and so forth could grow from the roof, but the plants could also just grow from the ground, underground. The fae could easily transport plants they like or can eat to their underground area, but some plants could make it down through their natural pollination.
Assuming the plants on the fae otherworld are similar to those on Earth, the fae would have likely evolved so whatever magical light they have synergizes well with the plants around them.
However, there is an issue here. In the real world, the plants get their energy from the massive amounts of sunlight hitting the planet. Next, low-level animals get their energy from the plants, then high-level animals get this twice-concentrated power from the herbivores. Now, you're saying the fae are powering the plants. That means they have to get that energy from somewhere first.
Under the guise of reality-check, this doesn't make a lot of sense using the natural order of things. If the fae subsist off fruits, or animals that subsist off the fruits, their total energy input has to be less than what they must output to keep the plants alive. The only way for this to work is if the fae get their "light" from some other energy source.
They could get it directly from the sun, but realistically, sunlight power is proportional to the area of your collectors. According to wikipedia, plants are 3-6% efficient. A fae could potentially be 33 times more efficient. If they have wings or something, they could spread them out and collect sunlight. Let's say their wings have about 2 m² of area, they're about 90% efficient converting energy, and the fae output light that's in the right wavelengths for plants, making their light about 2.2 times as efficient as sunlight.
Combining all those numbers means one fae could support about 4 m² of plant life. However, this assumes the fae stands outside all day like a plant would. We can get the energy at any given time of day using the calculations from PVEducation. I used the top applet, set the latitude to 40° (about where Denver is), and set the date to 25 March to get an average-ish energy plot.
Using the magic of spreadsheets, I used the data from the applet to plot energy absorbed versus the amount of time spent absorbing it. Since the highest power is at noon, I'm assuming the time is spent around noon. So 2 hours of absorption means from 11 AM to 1 PM solar time.
It takes about about 12 hours to get all the energy, but because there's more energy per hour in the middle of the day, you can get 25% in about 2 hours, 50% in about 4.5 hours or 75% in about 7 hours. This means one fae could support 1 m² at 2 hours/day, or 2 m² at 4.5 hours/day, with a little less in the winter, a little more in the summer. The fae could potentially store the excess energy during the summer and use it during the winter to keep the underground in perpetual spring.
Of course, if you start using magical power sources, anything goes. They just have to absorb more energy than the plants require, plus a bit more for efficiency losses. But you'll want to figure out what this magical power source is. It could be a glowing crystal they brought from the otherworld that behaves kind of like a nuclear reactor. They could steal "life energy" from the humans around them. They could have access to some kind of geothermal energy.
There are lots of plants and animals that live underground. These fae would probably have adapted for low-light vision, and they would sustain themselves on the various resources available.
Seeing as fae aren't real, a better way to look at it is "how do existing underground mammals survive?" The same provisions required to keep a rat alive are roughly the same as a fairy. If you're thinking fae are more similar to birds or butterflies, try to find animals like that.