OK, so among those six sensor choices, only the ones called system_1 and system_2 are for the general mobo, and suitable for case ventilation fan control. There is no information in the manual for which of those two should be used for case vent fans, so just pick one. The other four, including the CPU one, are all for specific components. They are useful only of you know where that components is and you have chosen to mount a fan aimed directly at that so you can concentrate some cooling there. Generally this is NOT needed.
The mobo comes with two optional thermistors, which are temperature sensors you can mount where you think you need to monitor a temperature. Each will have a 2-pin connector to plug into a mobo port, and the other end will just be a thin little metal tip. That is where the sensor is, and that's what you mount if you want to. Although the mobo will allow you to use these for controlling a fan, I do not advise that. First, it can be very difficult to mount a sensor so that it actually measures a component temperature you want, and to ensure that it is so securely mounted that it stays there and gives reliable info. Secondly, in almost all cases you have NO idea what the "correct" temperature for that spot is, so how can you decide to automate cooling there? However, you might want to connect those sensors and display something like the intake (room air) temperature, just for interest, without actually using that reading for any control purpose.
The fan headers you are using for the fans must NOT be set to Disabled / Stopped. THAT is why the fans are stopped! Change those to Enabled.
Sorry about the "DC Mode". That is another term some mobos use for the Voltage Control Mode, and that's how your mobo labels it. Since you have 3-pin fans, if the header each is connected to is configured to the new PWM Mode, they will run, but only at full speed all the time with no control. So set them instead to Voltage Mode, and the header can control their speeds.