Nice opening post, and a good set of questions Laika.
Most Serious Implications
They're all so interlinked that it's kinda tough to pick. However, I think I'll go with food shortages. If we have food available, then we can deal with people being forced to move around, we can deal with many other issues. But if we can't feed everyone the **** hits the fan pretty resoundingly. It is likely that areas without the resources that get desertified soonest, or which are soonest damaged by sea level rise, will produce big flows of refugees other places are gonna have to deal with, and those people need to be kept fed by the host area. Both for humanitarian reasons of course and because if they're not you'll have a large amount of disaffected hungry people in your country, which is tinder for the match of social unrest.
Likelihood as per Current Understanding
It rather depends how good we are at dealing with it. There are many contributing factors that damage our food supplies. These include widespread meat consumption, increases in ozone levels (quite a serious one, actually), more unstable climate patterns, salinisation of the soil caused by poor irrigation practice and by sea level rise, pollution with chemicals from industry and mining, resistance to GM technologies in many of the richest nations and desertification.
But we can deal with it, "we have the technology". A combination of high-tech solutions, proliferation of urban farming, better organised management techniques and changes in diet for the general population can manage this one. And that gives us a buffer to deal with other problems. Like water wars, mass migration, flooding and whatever problems humans are making up for themselves irrelevant of climate change.
Best Responsive Solutions
As far as food shortages go, I've already gone over it briefly above. In terms of mitigating the impacts of climate change - reduction of emissions is not enough, I don't think. If we drastically reduce meat farming and other main sources of methane production, then we can wait the 12 years until it decays. But other stuff like CO2, we need to get scrubbing to reduce the effects.
In terms of renewable energy - we already have the tech, and it's getting cheaper and better quickly. This is another area where estimates have proven conservative. There are major countries where it is the majority power source, and in much of Africa it is what they're switching over to as a primary source of electricity. Hydroelectric is big in Africa, and I reckon solar rollout will happen. This is already in motion, we are in the process of turning renewable, we just need to hurry it the hell along. But come on, ****ing Brazil is 84% renewable in terms of power generation, and some major African countries like the DRC and Ethiopia are over 99%. In looking at the list, North Korea is at 71%. Well done North Korea.
Space-based solar power and fusion may or may not show up at some point in the next few decades. But we can deal with it without them anyway.
Cleaning things up will require both technological and management solutions. For example, we're going to need to do reforestation programs. The problems is that the land where we might want to plant forest is often used for other things - this is another impetus for us to look into a) changing dietary habits and b) increasing agricultural efficiency. I think we need to tax the hell out of meat. However, there remains a high timber demand, and il/legal logging is an ongoing problem in deforestation. Improved forestries would be good, as they might undercut the demand which loggers are filling. This is particularly a problem in Brazil and Indonesia, I think. But also, technological carbon sequestration projects are gonna be needed, and quite possibly methods to scrub other bad stuff out of the atmosphere. We have the basic understanding about how to go about developing and improving such technologies, it is there, and we're getting better at it. By the time governments and/or non-governmental agencies get off their butts and do something about it, we should have the tech available for them.
Outside of that, there's a need for infrastructure to deal with the societal impacts. In particular, this relates to migrations of peoples, and their absorption into new areas. It helps that many of the areas that people are going to be migrating to will be those with severely ageing populations, including Europe, North America, Japan. This is assuming current trends continue - in difficult times, birth rates tend to rise, and this may well prove true as people are forced to deal with sea level rise in New York City, London, Tokyo... So we'll see how that goes. But these countries are going to have to get better at dealing with immigration and also develop new migrant settlement strategies alongside those already in place - for example, there are areas of the USA and Canada which are perfectly liveable but which have very low populations on account of a dearth of jobs, opportunities and stuff to do - setting up new towns here and plonking internally-displaced persons and climate change refugees from other countries there in large numbers may well be a good idea.