Hi there! My 4.25yo daughter is just the same imaginative (she spends the day being superheroes or doctors or lately, she's been a cat pretty frequently), VERY inquisitive and she makes connections that shock me. She understands the concept of death and get suddenly terrified at the idea that she might lose my husband or I. She LOVES math, everything has to be a pattern and she will stay up until 11PM reading "secretly" in her room!
She's been ahead since day one and forgetting she's 4 is pretty much an everyday thing (until the tantrums start & I forget she isn't really the 6 or 7 year old I think she is most of the time)...
I can't answer your gifted question, obviously, but I can say that you aren't alone!
