Can the Smart products learn infrared commands from, e.g., TV remote controls? If so, how do I do that?

Yes, it is possible. Please consult your user manual for this. In the system settings (SYS), you will find the menu item IR Menu (IRM) and below it IR Learning (IRL). Follow the instructions in the user manual and the on-screen menu. You will need the Canton Smart remote control and the infrared TV/universal remote control. With a Smart Connect 5.1 and the Smart Soundbox 3, this function is also accessible via the touch panel without the Canton Smart remote control.