Could I make my own USB Type A/A cable?

Sure. there's no reason you can't connect the two cable ends. It's probably not worth the effort, though, because you can order this kind of cable online for very little.

Yes, you can. You can even buy this on any online shop, simply search for father-father usb cable or similar.

But: the devices are communicating on usb on a master-slave protocol, and in most cases, master is a mother connector and the slaves are fathers. (Although it is quite possible to construct devices working on other ways).

So, although you can do this, it is highly probable that you won't be able to do anything with it.

Once in my life I've meet such a cable. It was used as a peer-to-peer usb network cable: plugging the both ends into the usb slots of 2 machines, it created a peer-to-peer ethernet over usb link. But in this cable, there were "something" (i.e. some active electronics) on the half of the cable.

You can also build your own devices around it, or it could be usable to solve some complex usb configurations (which are unlikely).