Jim, most all of your questions are answered in the DCS companion. I think you just need some more study. Perhaps take each of your questions, one at a time, and read everything you can find on the subject. If you're still confused you can then ask more specifically about what you don't understand on each topic.
I'm fairly certain inputs and outputs are one to one, but you can use one source to more than one input if properly sized. As for the difference in running command and conventional, that is pretty well spelled out in the Companion. When power is first applied at a TIU channel input, the TIU will start sending watchdog signals out to the track. If a DSC engine sees sufficient voltage and recognizes the watchdog signals it will start in command mode. If no watchdogs when voltage comes up it will start in conventional mode. You can use the remote to set channels to conventional or command.
Again, it's all there in the Companion. I do understand it feels a bit daunting the first time, but after you work through a few configurations things will start to clear up.
You must use fixed input #1 if you want to power the TIU from track power. Or, you can use a separate power supply to power the TIU. What I like about using the auxiliary power is that I can turn on the TIU and have that part of the control system up and running before applying track power. This make is easier for me to work on switch control with the AIU without needing the track power on. But it really works just as well powering the TIU from track power.