To some degree, yes.

No, there is no such thing as “psychic power”. Spidey sense is an adaptation of what a spider feels when something touches a web. It allows Spider-Man to detect danger before it happens and warns him of it in no time. The greater the danger or how close the danger is increases the tingling sensation.

Spiderman is not psychic; he does not predict or foretell events. He is not communicating with people that are in other dimensions or are dead. He is not a fortune teller.

His spider sense is probably considered a psychic ability, but only an instant before the danger occurs.
He cannot sense danger minutes ahead.

I’ve always been under the impression that it’s a metaphor for a spider’s many eyes, allowing the spider something approaching 360 degree vision. This would be a suped up version. Otherwise, his mere athleticism doesn’t really explain him dodging bullets. Though…other superheroes with less athleticism and no spidey sense do it all the time.

I definitely recall reading a spidey comic where they tried explaining it as a sort of limited precognition. I think it might have been a character like Destiny or something that tried to explain that Peter instinctively senses the future a few moments forward and then all the permutations and probabilities come back to inform how it helps him do exactly what is necessary to avoid the danger.

However, i just tried googling to find any canon explanation of his spidey sense and came up blank on the first page of results. I got a whole lot of hits…just none telling me a canon explanation. Though two did specifically say that the power is ‘deliberately vague’. So it’s possible that my remembered explanation was from something non-canon or was just my memory failing me.

No. “Spidey Sense” is a feeling mechanism based on physical and tangible things.
His “Spidey Sense” rivals mine.