Good questions, yes. I shall clarify.
Actually, both your ideas apply. Psychics, specially among the Terrans, have been trained/bred for such a purpose, to the point that some of them are quite powerful. Because of this most Terran warships are equipped with Psi-shields, as well as regular shielding. Ship shields, including psi-shields, are much more powerful than personal ones, due to the availability of power aboard a ship.
*Will be adding this to the info..*
Actually, both abilities you mentioned would be considered psi-power. A Psychic, however, is one that has taken one or more psi disciplines, and studied them carefully. The two you have mentioned, were clairsentience, and psychokinesis, respectively. Sorry to sound so brainiac-like, but I blame reading the old AD&D 2nd ed Psionics Handbook waaay too much for that.
Keepers tend to specialize in psychometabolism, I.E. healing and disease treatment, using mind power. It is also used for various 'buffs', usually on the psychic him or herself, but they can also be used on others.
Feel free to keep asking, I'll keep aswering.. and finding out what the answers are if I don't have them available. *grins*