I was trying to understand the channel's DC and AC coupling: DC coupling lets pass dc and ac signal; AC coupling blocks the DC part of a signal.
For example, here are the two coupling modes on the siglent compensation signal: with DC coupling we have a square wave 0- 3v, while with AC coupling we have a square wave + 1.5V / -1.5V.
That is correct for the square waves you are using. Now, if possible, repeat this with the same peak-to-peak amplitude but a 20% and 80 % duty cycle.
Two questions to understand:
1) to measure the real signal, DC coupling must be used. With AC coupling the signal is filtered (however in the circuit it is not filtered). So what use can AC coupling have?
Not all signals have DC components. The classic example is audio, which is from approx 30Hz to 20kHz.
It can be much easier to create amplifiers that don't have to respond to DC, since that means you can avoid offset and saturation issues. A classic example is accurately measuring low level DC signals, say 1uV, when practical amplifiers have much higher offset voltages. If you amplify the signal enough to be able to measure it, the amplifier output would be saturated against a supply rail. The solution is to "chop" the input signal, i.e. convert it to AC, amplify that without amplifying the DC offset, and measure the AC signal.
For simple measurement with a scope, consider being interested in the ripple on a power supply rail. You might be interested in seeing <100mV noise superimposed on a 10V rail, and that can't be seen when DC coupled since it would be at best 1% of the display's height. AC coupling "removes" the 10V, allowing the 100mV to fill the display.
2) in the DC coupling square wave compensation signal of the photo above, is the DC part of the signal represented by the low horizontal signal of 0V? Or is there no part of DC in this signal? (if there was a part of DC, would the square wave not start higher than the 0V?
thamks 
The DC part is the average (mean) value. Try changing the duty cycle to 20%/80%, and see what happens.
That raises the question of how long do you have to average. A
handwaving answer is that if you average for 1s then AC components above 1Hz will be removed, ditto 0.1s and 10Hz.
In practice the removal isn't that sharp, but often if you average for 10 times the longest AC signal period you will be OK. That's equivalent to the cutoff frequency being 1/10th that of your lowest signal frequency.