I've been thinking on this for some time concerning a personal attempt at writing a novel involving individuals with such powers and how a society would exist and function with such people being common place.
There is currently a popular theory being explored called the "Morphic Field" theory which in essence involves the recently discovered behavior of "Microtubules" within neurons. It is surmised that each set of Microtubules is actually capable of quantum computing. When we start talking about quantum computing we start thinking of quantum entanglement with its' surroundings. Hence the "Morphic Field" of influence thought to exist around the human body according to the theory.
Einsteins' description of quantum entanglement was "Spooky Action From A Distance". I'll leave the rest of the speculation up to your imaginations as to what may be possible if we just end up thinking in the right way.
However there may even be an evolutionary explanation as to why and how certain sixth senses could come to be. Especially that of precognition and possibly the perception of ghosts and spirits. It would be very advantageous with respect to survival if that small little rodent 60 million years ago actually knew that one of its' fellow rodents had just died a horrible death nearby due to a lurking predator. The more a Rodent can sense this fact with maybe even just a sense of foreboding. The more likely it is going to be that it decides that taking that particular route may not be a good idea and the more likely it is to live long enough to have progeny with similar skills. Quite logical when you think about it. How that mechanism actually works is open to speculation but it really could be that now expired rodent a). left a message/recording of its' fate in the surrounding environment through quantum entanglement under duress/stress that rodent b). could play back.
There is also one other possible method of at least transmitting milliwave signals (milliwaves are something we are only exploring electronically now due to it's being in that zone between microwaves and infra red for which neither type of sensor works very well). Namely each and every cell of the human body has a series of symbiotic passengers called Mitochondria and if it wasn't for those Oxygen would be poisonous. The more oxygen and energy a cell needs the more mitochondria it has. Transmitters and receivers of energy are called transducers for a reason in that something like a loudspeaker can also act as a microphone and an Aerial can be used to both transmit and receive. The simplest electromagnetic Aerial is a conductive loop and guess what... Mitochondria are conductive loops of circular DNA. Yes DNA conducts electricity and would generate a small circular current dependent on how active it is at the moment. Brain cells need more oxygen than anything else (apart from maybe the heart and liver) and would generate a small EM field in the milliwave band in response to how active they are. Current brain scanning technologies can already use blood oxygen consumption to detect certain cognitive processes though at present they can only tell the difference between a couple of different thoughts.
The speculation could go on. However one thing that is certain is that things like PK and ESP are certainly not "Impossible".