I now have looked at the aquilegias in our garden. First I have to climb down and say that we do have different types of flowers on the same plant. I have one which has double flowers on one stem and single flowers on the rest. And several which show any number (0-5) of spurred petals on different flowers on the same plant. And another where the bud reminded me of the description you gave as being like a fritillaria, where the spurs were tucked behind the outer petals in the young flowers, but became visible as the flower matured.

I think I may have seen the difference in your second question - flowers with a central spire completely hidden by fat anthers making a cone-shaped heap, and other flowers, and others with a central spire surrounded by stamens with tiny dark coloured anthers on top. As I thought, that's a maturity thing - the second type are on older flowers, where the anthers had withered, and to demonstrate that, I also found some intermediates, with anthers one side withered and the other side looking like the cone-shaped heap of oval bits.