Full spectrum LED grow lights are lights with balanced spectrums that have energy ranging from ultraviolet to infrared, just like natural daylight. They use a phosphor coating that takes lighting from a narrow wavelength range such as a 460 nm blue and convert it to a wide range of longer wavelength light such as a 600 - 700 nm red for crops' flowering stage. And the blue LED can be coated by the mixture of green, yellow and/or red phosphors. All these colors make up what we call the full spectrum.

Yes they do actually work. You grow plants indoors will have to provide the amount and quality of light as they are provided by the sun. While the full spectrum lights include all wavelengths of visible and invisible (UV & Infrared) light that inhouse plants need for photosynthesis. In some cases, full spectrum grow lights are designed to replace direct sunlight.  

Full spectrum lights has similar the proportions of Blue, Green and Red lights to the sun so they can be used as grow lights for indoor crops. 

There are three main types of grow lights:

1) Fluorescent lights
2) high-pressure sodium (HPS) sometimes referred to as HID (High intensity discharge)
3) light emitting diodes (LED)

These three main categories of grow lights have their own spectrum. But full spectrum is the one that contains all of the colours of light for plants to grow.

The ideal spectrum for plants growth is the one that is different by species. Plants will need different color of light at different growing stages. For example: plants performs better in the vegging stage with more blue light wavelengths because blue light increases overall plant quality, resulting in leafy plants that can support plenty of budding and flowering. Red light promotes budds and flowering, but plants grown under only red light or too much red light will become tall and stretched. So full spectrum lights have certain amount of blue and other colors of light added in to balance out the red light. 

Seedlings need the least of light and most hanging distance between the lights and the seeds. As they are young and delicate and easy to be burned, so it is safe to keep your lights up to 24-26 inches during the seedling phase of growth (first 3 weeks), and 18-22 inches during the vegetative and flowering phases.

Not all LED bulbs full spectrum. If the LED is white then it's full spectrum because white light is made up of light in every color. 

LED grow lights provide a better spectrum, consume one-third of the energy, and offer a product that will last 10 times longer than any HPS or CFL grow-light.

LED grow lights will not "fail" or "burn-out" like HPS or CFL. They are more reliable, efficient, and longer life-span.

LED grow lights will reduce air-conditioning expenses because of their heat-reduction properties.

LED  grow lights do not have necessity to change bulbs from time to time.

No, grow light should have its own/different spectrum for plants. Plants have different requirement for lighting at different stages of growth.

Seedling / Clone: around 300 PPFD

Vegetative: around 600 PPFD

Bloom / Flowering: around 1050 PPFD

Generally speaking, you should keep your LED grow light 24-26 inches away during the seedling phase of growth (first 3 weeks), and 18-22 inches during the vegetative and flowering phases.

In the seedling stage, plants require between 200-300 umol/s.

In the vegetative stage, plants should receive 18 hours ON and 6 hours OFF of light and require between 310 and 620 umol/s.

In the flowering stage, plants are receiving 12 hours ON and 12 hours OFF of light should receive between 460 and 930 umol/s.

Full spectrum is the best for indoor plants because it has a balanced spectrum output of the light to match the natural sunlight. It also provide enough amount of light to meet plants need in the each cycle of growth. 

There are three main types of grow lights:

1) Fluorescent lights
2) high-pressure sodium (HPS) sometimes referred to as HID (High intensity discharge)
3) light emitting diodes (LED)

Most popular LED grow lights for vegetative stage is 18 hours on and 6 hours off. When approaching the plants' flowering stage, most gardeners will reduce their light to 12 hours on and 12 hours off.

1 x 1 feet:  20 watts for 2 plants in veg stage  | 30 watts for 1 plant in flowering stage.

2 x 2 feet:  80 watts for 4 plants in veg stage | 130 watts for 2 plants in flowering stage.

3 x 3 feet: 180 watts for 9 plants in veg stage | 270 watts for 5 plants in flowering stage.

2 x 4 feet: 160 watts for 8 plants in veg stage | 240 watts for 5 plants in flowering stage.

4 x 4 feet:  320 watts 16 plants in for veg stage | 500 watts for 9 plants in flowering stage.

4 x 8 feet:  620 watts 12 plants in for veg stage | 980 watts for 18 plants in flowering stage.

5 x 5 feet:  500 watts for 25 plants in veg stage | 760 watts for 12 plants in flowering stage.

6 x 6 feet:  720 watts for 36 plants in veg stage | 1,060 watts for 20 plants in flowering stage.