1: Your chakras are already open. Your life energy flows through them so if they were actually closed you’d be dead. When people talk about “opening” their chakras, what they really mean is developing them to handle more power.
2: Chakras are imaginary; they don’t exist in any real sense. They became part of the Western Magical Tradition by way of Theosophy, whose founder, Helena Blavatsky, was enamoured with all things from the “mystical East,” and then the New Age revival of the 1960’s got a hold of them and they became ubiquitous in the occult.
3: There are different numbers of chakras, even within the yogic traditions themselves. Other traditions, like Tibetan Buddhism, also have their own versions.
4: As for enhancing psychic abilities, yes, working with the chakras are said to do so. They are also said to confer powers, or siddhis, like levitation, teleportation, and the ability to shrink, upon practitioners when fully developed. The aim of yoga is to become a “perfected” individual, however, and the powers are seen as a distraction so students are often told to ignore them.
5: Kundalini is the Sanskrit term for the sexual energy of the body, said to lie sleeping at the base of the spine, and often described poetically as a great serpent. By awakening this energy, and bringing it up into the brain, it energies and powers up the entire being, including one’s spiritual bodies. It is known to enhance cognitive function, as well as physical capabilities such as speed and strength. It is an infinite energy circuit, and once set into motion, it becomes stronger the more you use it. It is considered to be very dangerous, and can cause actual physical damage if not done properly. Taoism has a similar concept, called the Greater Kan and Li.