The control between normal and primed axes is I believe under the control of the microcode, not the cards themselves (refer to Bromley's detailed analysis). One of the masterful aspects of the later AE designs were the multiple communicating state machines on separate barrels which managed the ingress, egress, and mill axes. See particularly the pipelined multiple add/subtract operation.

Regarding the format of variable cards and „address decoding“, Babbage tried different schemes at different times, ranging from binary encoding to „one hot“, or even „n hot“. For instance there is a place where he counts the number of holes needed for a store of some size (1000 variables I think), and it clearly indicates binary code. On the other hand, in one of the letters to Ada when she was working on the notes he explains how it's possible for a value from the mill to be transferred simultaneously to multiple store locations. Since it's simultaneous, it must be under the control of a single card. That is possible if there are distinct holes for each storage location - just punch several of them, then multiple columns will be raised simultaneously to receive the value. He also comments that obviously, the inverse operation (ie sending multiple columns to the mill simultaneously) is not possible.

Regarding number cards, there is a description somewhere (probably in the notebooks) where Babbage describes how a problem is run on the Engine. It begins by reading a bunch of number cards to initialize locations in the store with the constants and initial data for the problem. I have always assumed this would involve the use of variable cards to select the locations to receive the value, but he was not explicit on that. I'm pretty sure he considered „I/O“ devices (eg number card reading, number card punching, printing etc) as part of the store subsystem.

Regarding card control, Bromley's analysis of the microcode for the great operations gives some insight here. It's much more subtle than just saying the operation card puts the mill in a particular mode, because holes on the card can be sampled at various points during the execution of the microcode for the operation. This is one of the ways Babbage was able to make the microcode so incredibly compact, because it permits a great deal of sharing of the verticals on the barrels.

There is inconsistency in the various descriptions of how things are coordinated here. While the Sketch does imply it's the store sending things to the mill which then consumes them, it cannot really be that simple, because for example in division, which needs one double length operand and one single length, three variable cards are going to be needed, but there are only two sets of storage on the ingress axis, so the fetching of the third location cannot possibly happen till the operation is already underway. And remember that Babbage was forever trying to optimize performance so he wanted to make use of the first operand as soon as it had arrived on the ingress axis.

Regarding backing of cards - this was controlled by card counting apparatus (several sets), but just how these counters are initialized under various scenarios is unclear.