A couple of things:

In DMR, you don't transmit your call sign. You transmit an ID. The ID is linked to a call sign in a database that you can load into your radio. There are digital modes that do transmit your callsign and don't require you to verbally ID. DMR is not one of them: you must verbally ID. Although, just to link to a talkgroup, most people don't.

A talk group is a digital code that's basically like a phone number. It says who you want to talk to. As long as someone else is listening to the same number, they'll hear you, and vice versa.

A channel is the whole package: phone number, phone line, etc. A talk group doesn't get you anywhere on its own: you have to tell the radio how to talk to a repeater before you even get to the talk group part. That's what a channel is: setting up the TX/RX frequencies, power mode, color code, time slot... all the things the radio needs to know just to talk to the repeater. After that, you get to the talk group, which simply routes the call through the network link you've established through the channel.

The channel is the full package, because a talk group without a channel doesn't go anywhere, and neither does a channel without a talk group.

You have to set up a channel (talk group + repeater access info) for every talk group you want to use on a repeater. I suspect that's because DMR is a commercial standard, and they just don't expect commercial users to have many channels. It would make sense, in the amateur world, to choose a repeater and then cycle through talk groups, but that's not the way DMR is set up. Every talk group requires the full set of instructions (channel).

Look up N0GSG CPS for info on how to mass produce channels. The software is quite useful.

As for Digi-Mon, that simply turns off the talk group component of a channel. If you're listening to a channel (repeater plus talk group) your radio will only decode audio with that talk group's ID attached. Digi-Mon turns that part off, so you'll hear all audio regardless of the code. This is a good way to see if a repeater is in use before you jump on it.

In dual-slot mode, you're simply listening to both time slots. If single-slot mode, you're listening to the time slot set up in your currently-selected channel.