they have the spines to protect them from your face
Yes, cactus spines are living parts of the cactus plant. They owe their existence to growth buds on the plant's surface. From the growth buds also come a cactus plant's flowers.
The pointy things on a cactus are called spines.
The 'spines' of a cactus attach directly to the stem of the plant.
There is no cactus capable of shooting its spines.
a cactus
Cactus
That's a cactus
One of the many cactus species
A cactus has no leaves but does have a stem.
Spines protect the plant from animals that would injure it. They also provide some shade for the stem of the plant.
Spines: Spines help the cactus in several ways. The most obvious use of the spines is for protection against foragers. The cactus basically states "How much pain are you willing to indure to get a drink in this desert?"; Surprisingly, some animals do partake. In some cactus varieties the spines participate in water collection. Water from dew condenses on spines and, in some cactus species, downward-pointing spines help to direct rainwater to the roots of the plant. Spines help to reflect light away from the cactus stem theoretically lowering the stem temperature. Some spines also trap in a layer of air next to the cactus stem preventing loss of water via evaporative cooling.
No, a cactus does not have a thorn. A cactus has spines.