Aquilegias are good at producing a wide range of flower types in their seedlings, from the "clematis flowered" type with flat petals through to various degrees of double-ness. I don't think there's much "purpose" to it. Better to ask the purpose of the spurs, which are nectar containing, thus limiting pollination to long-tongued insects (because the pollinating insects come to the flowers to take the nectar) . The advantage of limiting pollination to a smaller group of insects is that the insects themselves will be feeding on a smaller range of flowers (those which require a long tongue) and so there's a greater chance your pollen gets taken to another aquilegia and not, say, a rose.

The flat flower type is more typical of other plants in the same family, eg clematis, buttercup.

But I've never seen two flower types on one plant.

As to the second question - aquilegia don't have separate male and female flowers - both male and female bits are in the same flower. Have you considered that the flowers might not be the same age? I haven't looked at aquilegia flowers closely enough so haven't seen what you are asking about, but wonder whether the stamens devlope first, then die back when they have shed their pollen, allowing easier access to the stigma - a mechanism to avoid self-pollination? This is speculation. I really should go and look at some aquilegia flowers first.

You're right though that when the male and female flowers are separate (eg Skimmia, where they're on separate plants) the males are the ones with fluffy stamens, and the females have a knob-like stigma. Primroses do it a bit differently. All flowers are bisexual, but some have the stamens longer than the stigma, and some have the stigma longer than the stamens, so that if you look without dissecting the flower, you can be forgiven for thinking there are separate male and female flowers.