Telepathy: Telepathy (or rather, techlepathy) is a somewhat limited faculty, as described under Psychic Powers. Being essentially a way to transmit neural gestalt information over WiFi, it is an excellent messaging system, complete with the ability to transmit images, emotions, information constructs, and other non-verbal information, and communicate broadcast/narrowcast, local/distant, private/conference, etc., etc., and even to synch up well enough to form a conflux (see: Mental Fusion).
It doesn’t, however, let you overhear people’s thoughts (unless they’re sloppy and accidentally broadcasting, which does sometimes happen), go in and pull thoughts out of their heads (you want a SQUID for that, or a mind-state reader of one sort or another), control minds (although you can inject the same memes as you can over any communication channel), or enable the rest of the assorted magical aids and attachments (dream travel, astral projection, and so on and so forth). It’s also, being EM based, limited to the speed of light.
Since it’s harder to fake all the sidebands, a telepath can sometimes be something of a Living Lie Detector, but reliability in this role still isn’t great, and you are almost certainly better off with a regular mechanical alethiometer (which uses a SQUID).
Electronic Telepathy: Specifically, the kind built into the eldrae and galari (although with different encodings, originally), and put on general sale by a number of corporations. See Psychic Powers.
“Are you sure this will work?”
“Well, no, it’s an experiment.” Brandel held up his hands, warding off the glare thus produced. “But the theory is sound. We’re never going to find out more unless we move it in vivo.”
“The theory is barely formed.” Soléä gestured at the triboard with her half-eaten sandwich, before noticing and setting it down on the lab bench. “The kinesis effectors were designed to work with a specific neural architecture, and a fully sophont one, at that, and we only barely understand how they work. You think they’re self-modifying to optimize for the specific host brain, but this is a whole other order of difference. Do you really think they’ll be able to adapt to that?”
“Their neural architecture isn’t so different from ours. And I think the effectors might, yes. They’ve proven remarkably versatile in the past.”
She snorted. “You’ll be lucky if they just don’t work.” Her hand fell to the bench, came up empty. “Where’s –?”
On the other side of the lab, the first of the test subjects swallowed, flipped his ears, favored the researchers with a canine grin, and went searching for any remaining sandwich crumbs as the photon-discharge corona faded around him.
“…I withdraw my objections.”
Conveniently Coherent Thoughts: Subverted; the reason you can get some coherent thoughts and images through the techlepathy part of the Psychic Powers is because they require you to produce specifically focused thoughts and images in order to engage the transmitter, in a similar way to a voice-activated microphone.
If they just transmitted your regular thoughts as they happened, the telepathic bands would be filled with not merely a rambling narrative thread of consciousness, but pure neural hash from the thousands of different threads in your mind all talking at once.
Psychic Powers: Of course, there is absolutely no such thing as psychic powers. Don’t exist. No place in a rationally organized universe, like any relatively firm-to-hard SF universe. Can’t seriously believe otherwise.
But that said…
Telepathy/Empathy: Do you believe in wireless networking? Evidently the Precursors did, and they really hated waiting while runners were sent or shouting was done, because they built this one right in to the brains of their favored manufactured race. If you want to detect telepathy, you’ll find it in those weird screebly neural-gestalt signals hanging about in the high microwave part of the EM spectrum.
Precognition: Do you believe in clionomy? (On the large scale, the gentle art of computing statistical predictions concerning the future of organizations and societies.) And very advanced predictive algorithms? (Because with a computer in your head and advanced enough body-reading, simulation and prediction software – and maybe a little SQUID use – you can read people and predict their future actions in a downright spooky manner. Especially when done in combat.)
Psychokinesis: Do you believe in implanted vector-control effectors? Another fun now-reverse-engineered Precursor leftover tech, these tiny nervous-system-integrated nanopicosomes are all you need to toss gravomagnetics around, fetch yourself drinks without standing up, indulge in wuxia wire-fu, and kill people with your brain to your heart’s content.
All available in stores for the usual enhancement prices, should you be unlucky enough not to be born with them built in…