I consider myself an "open-minded skeptic" (contradiction in terms, but oh well).
I'm a perfectly articulate, intelligent, grounded person not given to flights of fancy. Yet I have experienced some pretty weird shit I must admit. I'm a bit reluctant to share much detail but like you I have had vivid premonitions and bizarre clairvoyant dreams. I have put most of that down to medication - it feels real and different to to normal dreaming, but that's the only scientific explanation, that my brain is fucking with me. 
I have had a private reading and been to a small clairvoyance evening - not of my own volition, truthfully, but because my very lovely friend lost a child (and rightly or wrongly, takes a lot of comfort from such readings) and I agreed to accompany her.
I tried to be open minded with the reading, and it was sort of fascinating. She came up with information that I simply can't fathom she could have got from basic research on my name or family, and which was rather too specific for her to have been cold-reading. Sure, throw enough out there and she'll get a hit or two, but she was very succinct and specific, not vague at all. I checked something afterwards and she was correct, I actually hadn't known for sure but my mother confirmed it.
The evening was more vague and I was very much more skeptical about the other readings I observed from an objective perspective.
I am not a complete non-believer, I prefer the notion that there is something in it - I figure that I partly believe because I choose to, not because it can't be proven to be fake.
The sensible scientific part of me says it's all bollocks though.