The cactus is suffering from poor growing conditions, probably especially in winter, where it is seeing too much cold, moisture, and humidity. It is not enough to kill it outright, but it looks like it gets some kind of fungal affliction damaging any new growth that it may have had during the warmer months of the year.
I think what you are seeing in the last picture is the plant forming 'bark' on the parts where it is not able to maintain active growing areas or areas that contribute to the plants respiration, so no need to maintain the outer skin like you see in the new growth areas - it happens to older cacti, though in some cases this can be a sign of corking disease, which can kill a plant.
If you are unwilling to keep the plant as is and pot it up into a somewhat bigger pot with fresh well draining cactus soil, then I would suggest taking cutting of whole 'arms' or sections, not just the new growth for example the 'branch' that is visible in the last picture would be a cutting point. Doing that would give the plant a solid base for rerooting and new growth. I would probably do that given that if this plant keeps growing the current base is not going to be that stable long term, but it is not going to matter or change much unless you improve the plant's growing conditions and how you winter it.
It looks like a myrtillocactus.
