Is narcolepsy a type of insomnia?

No. People with narcolepsy do have disrupted sleep, but it is not the same as insomnia. With insomnia, people have a hard time transitioning from wake to sleep, resulting in tossing and turning, frustration, etc. However, once asleep they usually sleep well. With narcolepsy, the transition to sleep occurs quickly and at inappropriate times (during the day, with activities). Other symptoms also occur.
No, it is different. Insomnia is: 1) difficulty falling asleep; 2) difficulty staying asleep; 3) a combination of both. Narcolepsy is a physical disorder associated with a chemical imbalance in the brain that creates: 1) excessive sleepiness; 2) loss of muscle tone when emotional (aka cataplexy); 3) sleep paralysis and/or hallucinations. Treatment can be medicine.