Those are the four groups and it seems most likely that flight evolved only a single time in each group. Flight may have been lost and reacquired in those lineages but it seems that all insects, birds, etc. descend from a single flying ancestor.
I find this unlikely. The insect wings share almost nothing in common with the rest of the animals.
The wings on the pterosaurs, bats and birds all come from a common trait. But that common trait are their extremities. The actual wings are a variation of their extremities. The wings of the birds and the wings of the pterosaurs differ a lot, so I'd assume that the actual wings developed independently. The bat, the pterosaur and the flying squirrel wings might have common genetic origin to some extend, but that doesn't mean that they didn't develop independently.
On a monocellular level. Rotating wheel-like structures can't exist in more complex organisms for reasons already stated upthread.
I believe that it's more appropriate to say that they can exist, but the evolutionary development of such is unlikely. However, if the universe is swarmed with life, maybe on some planet somewhere some species did develop them.