As far as insights and information goes, that's an every trip occurance for me. I always have some sort of crazy new idea or way of looking at things after a strong trip.
Special abilities are another story and it's something I've thought about in depth. There have been only a few times I've noticed some type of extrasensory perception, but it was so subtle and fleeting that I could always count it as coincedental or a product of a hallucination, but I'll share them in the hopes maybe others have noticed a similar thing in their own voyages.
The first time I experienced anything supernatural was some type of psychokinesis, but this could very much be attributed to my senses being all jacked up from tripping so hard. Anyways, I was watching Heroes the tv series on my laptop and I've always loved the character Sylar. For those unfamiliar with the show, Sylar is a super powered serial killer who uses telekinesis as one of his primary abilities. Well I had this strange idea as I was watching the show in a deep trance state that I should be able to access similar abilities myself while on psychedelics (at this time in my explorations, I would take large doses of mushrooms and see if I could manifest my own thoughts, this was a series of pseudo experiments I was working on a year or so back). Don't ask me why I thought this, but that was my intuition at the time 'you can do that too ya know'. So, in a heavy trance state I held my hand out towards my open bedroom door and pushed with my entire mind willing the door to move. I kid you not the door actually closed! However, when I went to recount this seemingly miraculous event later, my mind sorta kept telling me that my latent telekinetic abilities were a product of my hallucinating mind and since there was no one around to confirm what had happened, and due to a lack of any other sort of empirical evidence that this actually happened, I've always wrote this off as a false memory.
The only other sort of paranormal ability I've manifested would be telepathy, and this one I take more stock in since others report similar things especially while on ayahuasca. I had this one experience where I was tripping with a few friends by a lake around a fire. As we were all peaking, my mind recalled that some people experienced telepathy while tripping in groups so it occured to me to try this out for myself and see if there was any merit to these claims. I was sitting close to the fire and thought I would try to send my friend who was sitting next to me a message with my mind. The extent of the message was simply 'Hey M, can you hear my thoughts?'. My friend M turned to another person in the group and giggling wildly (he was really, really gone at the time) exclaimed 'Guys... does anyone else feel like someone is reading your mind?' to which was met with laughter by the rest of the group, however to me it was a sign that communicating via mind speak could be possible on psychedelics, even though I apparently didn't do it right (M didn't recieve my message as I intended it, although he got the impression that someone was in his head which was sort of a success imo).
The only other time I experienced a form of telepathy was extremely random and in a different setting entirely. On my most profound spiritual trip, the trip that to this day I claim changed my entire life, I had a telepathic exchange with an entity from hyperspace while I was still in my bedroom. My girlfriend and I were in my room both coming down off a really large dose and in this specific trip I had been told that everything is a part of me and that my physical body is just a toy. As I'm having this mental conversation with this entity, I look at my girlfriend who was doing yoga on the floor and I asked the being 'what about her? is she just a part of me as well?'. The entity responded with 'yes. what you love in her is what you love in yourself. her body is just a vessel... it's the same as yours.' No sooner do I get this telepathic message that my girlfriend sits up from the floor and looks at me and asks 'what's a vessel?' I shit you not this was within seconds of hearing this in my mind! Very stunned, I asked her why she would ask me that and she responded by saying 'I dunno, I just had this thought that my body is just a vessel... but I don't know what the word vessel means!' to which we both had a good laugh.
To me, it definately seems that developing certain paranormal abilities might be possible through psychedelics but in all my experiments where I was actually trying to manifest these abilities, these three events are the only times I've ever had them show up which leads me to believe I'm doing it wrong somehow. I imagine a shaman who is well-traveled in hyperspace might be able to bring back with him the supernatural abilities they tend to be known for. This seems possible to me, although I would have no idea how one would do it.
All posts are from the fictional perspective of The Legendary Tek: the formless, hyperspace exploring apprentice to the mushroom god Teo. Tek, the lord of Eureeka's Castle, is the chosen one who has surfed the rainbow wave and who resides underneath the matter dome. All posts are fictitious in nature and are meant for entertainment purposes only.