What are the benefits of having one more leg section? Being I am 175 cm tall, I will never use the legs fully extended on a plane.

More sections reduces the length of the tripod while folded. This is most desirable for travelling. As a side-effect, there is a slight loss of rigidity since the extra tube is more narrow and maybe a more time to setup. Given this main reason, I have always chosen more sections since size is a primary concern for me, even more than weight,

Is carbon fibre really more stable than aluminium?

There is no such claim. Carbon fiber is more rigid per weight. So, if you are comparing tripods of different weights, you will have to go with the specifications on maximum capacity. Conveniently, both your choices are from the same manufacturer, so they are comparable as they are most likely to use the same testing methodology.

Does 0.5 Kg make a big difference in terms of overall weight? I am not a professional photographer. My heaviest gear consists of a Nikon D610 and a Tokina 11-16, no extreme telezooms.

0.5kg is 0.5kg more to carry. That's it. Weight adds up but you have to decide yourself. Add 0.5kg (about 2 cans of soft-drink) to your bag and see how it makes a difference after a day shooting.