Is there a reason that many priest spells, especially shadow priest spells, have names that refer to psychic phenomena like " [Mind Spike]" or " [Psychic Horror]"? Are priests implicitly telepaths?
The Light is often said to bring about feelings of positive emotion— hope, courage, comfort— and the like. Shadow abilities are just the opposite, able to impart feelings like despair, doubt, and panic. In a poetic sense, it can be said that the emotions which the Light brings about come from the "heart," whereas the emotions manipulated by shadow are often based on survival logic, and therefore affect the "mind." That said, priests and their abilities are not necessarily always psychic or telepathic in nature.
When undead use or are healed by the Holy Light, does it cause them any actual damage or harm, or does it only cause them pain (in addition to the intended effects of the spell)?
Channeling the Light in any way, or receiving healing from the Light, only causes pain. Forsaken priests do not disintegrate or explode from channeling the Light for an extended period of time… though they may wish they would.
Are there long-term effects on an undead who is in regular contact with the Holy Light in a positive way?
It is difficult to say, as there are no known records of undead wielding the Holy Light before the Third War. There are reports, however, that some Forsaken have slowly experienced a sharpening of their dulled senses of touch, smell, etc., as well as an increase in the flashes of positive emotions that have otherwise become so rare since their fall into undeath. Unfortunately, this may be the cause of the Forsaken priesthood's increased attempts at self-destruction; regaining these senses would force the priests to smell their own rotting flesh, taste the decay in their mouths and throats, and even feel the maggots burrowing within their bodies.