Population: I agree, we are starting to come to terms, as a species, with the limits for our growth that the planet imposes upon us. Fortunately. However, we might always come upon further hacks that extend our food supply, and the trends of today can turn back up as we push back the limits further. But I find that unlikely.
Climate change: for this case I would quote you out of context: "the future looks questionable globally". Our emissions will peak, yes, but constant emissions will still mean a continuing accumulation of carbon in the atmosphere. We need a complete reversal of the emissions growth, through an absolute elimination of emissions, into a net negative emissions scenario, for decades, starting in just 20 years - just to reach a stability in the carbon concentration! That is batshit crazy stuff. The only thing that a stabilization in population brings is a stabilization in emissions, and only with technological advances since even a stable population will expect a growing economy and consumption. Unfortunately, a stable population as civilization exists today is not compatible with a stable climate. The two are at odds and we will need much more effort to justify our long-term presence in the biosphere.
Which brings me into the theme of overarching patterns. The S-curve and the likes may describe a singular change over a limited period of time, but the story never starts or ends there. Products take a long time to come into being, they are based on other products and other technology, they arise out of a setting. Then their success may feature an S-curve. And eventually, the products will be obsolete, broken, forgotten, and new products take over. The end is exactly that – the end. But the world does not end, it keeps being dynamic, it keeps changing, and that ever-present driving force will kill that which stagnates.
The stagnation of culture can be theorized to be a symptom of impending decline. This is an ancient theory. Maybe we really are going to see a death of cycles, a triumph of linear theories? But I find also this unlikely. Socio-political changes are obvious in today's global world, and these power shifts tend to send nations and regions into new cycles, some of decline, some of growth, and sometimes we see drastic changes in-between. Stagnating regions will have trouble in these times and are more likely to burn fiercer when the time comes. I am worried for the continuation of the stability that we have known in the western world for so long. I believe these regions are in a stagnant phase and in a hundred years or so, things could be very very very different. I only hope it won't happen through widespread conflict, but rather through short periods of destructive change that we will rebound from and regain enough plasticity to adapt to the changing world.
If only we had a well-developed framework of Psychohistory!
EDIT: Also, technology. Significant breakthroughs in AI, quantum computing and other known and unknown technologies could be potent enough to change the rules of the game, upsetting any current S-curve trend or other trends.