Since human cognition is based from previous cognitive state and interpretation of sensory input, precise communication requires mapping the communicative symbols as closely as possible to your desired semantics.
Earth itself will do just fine at any temperature that's below literally evaporating. Various life on this planet has evolved to thrive in wildly disparate climates, and short of complete eradication of an ecosystem, surviving organisms both tend towards better suitability for their given environment and adapt their environment towards better suitability for them (both with limits). We humans should be looking at what temperature ranges would be the most beneficial to human society as a whole. Sure, that's incredibly self biased, but as a human, I contend that's an incredibly useful bias to have.
My starting point with that question is to say humans are best suited to the global climate under which they evolved. Muck about with that at your peril. Try it out on the hot-spare planet first please.
Attempting to adapt the environment will have unforeseen, probably serious, consequences. I for one hope we do not try, or have no choice but to try, geoengineering attempting to avoid catastrophe.
I completely agree with your first point. One of the key problems is that humans are the most adept species in billions of years at adapting the environment. Over time, the more likely a thing is to happen, the more that thing does happen. Adaptation is most likely to occur in the form of adding energy, and as Applejinx noted elsewhere in this thread, adding energy to a chaotic system increases its degree of deviation.
Quite, and we've never tried geoengineering on a global scale. We've had enough problems from localised changes from agriculture or introduced species.
To your second point I've always preferred climate change as a term over global warming as some areas will end up cooler, others more changeable. Especially if one of the major ocean current systems slows or stops.
Earth itself will do just fine at any temperature that's below literally evaporating. Various life on this planet has evolved to thrive in wildly disparate climates, and short of complete eradication of an ecosystem, surviving organisms both tend towards better suitability for their given environment and adapt their environment towards better suitability for them (both with limits). We humans should be looking at what temperature ranges would be the most beneficial to human society as a whole. Sure, that's incredibly self biased, but as a human, I contend that's an incredibly useful bias to have.