Relationship between natural disaster and global warming, in the media
First thing first: It is very hard, if not impossible, to attribute a single anomalous weather event to climate change. The weather exhibits a huge amount of natural variation.

The recent spate of cold weather that recently has hit the eastern part of North America is consistent with climate change and has even predicted to be a consequence of climate change. However, this spate of cold weather is also completely consistent with natural variations in the weather. As noted above, it's very hard to attribute a single weather anomaly to climate change. Winter weather is, by its nature, extremely variable.

It's also important to remember that this cold weather is a local event. Europe and Asia have been quite balmy this winter. Do not be surprised if December and January turn out to be considerably warmer than historical values when averaged over the entered planet. And even if it isn't, that does not falsify climate change. Climate change is about what happens after removing short term variations ("years" is short term) from the equation.

Note that I have been consistently using the term climate change rather than global warming. It's not that global warming is an incorrect term. People mistakenly take global warming to mean that every single day will be warmer than it was a year ago, everywhere on the planet. The science does not say this. As noted above, the recent spate of cold weather that has plagued and continues to plague eastern North America is completely consistent with and has been predicted by climate change (or global warming, if you will). But it's also consistent with natural variations.

That said, at least one event during the last year most likely was amplified by climate change, and that would be the huge amount of water dumped on southeast Texas by Hurricane Harvey. Tropical cyclones (e.g. hurricanes) and even very strong ones, are natural occurrences. Climate change does not predict that we will get more tropical cyclones. It does however predict that they will get more severe as the Earth warms up, on average. The huge amounts of water dumped by Harvey are consistent with and predicted by climate change, but not so much consistent with natural variations. While Harvey itself wasn't caused by climate change, a sizable portion of the 52 inches of the rain that it dumped most likely was a result of climate change.


Update, since I didn't directly address the questions raised

One reason I didn't address those questions is because the original post has too many questions (Martin: Please read up on how to write a good stackexchange question.) I'll focus on a couple of them.


  On average, is the media doing a fair and balanced job as an educator of under-informed people (like myself) on that topic?


The first of the cited reports in the question has the teaser headline "Flooding in Paris Maybe Due To Climate Change" -- but the link does not discuss that at all. The news report merely covers the fact that Paris is currently flooding. (Perhaps a once longer version did cover a potential link to climate change.) This is a disservice because a potential link between flooding in Paris and climate change does exist. In particular, climate change has roughly doubled the probability of severe flooding events in Paris.

The second cited article is much better. It does not attribute the late December / early January cold snap in the US to climate change. It merely states facts. One fact is that many people (including the president of the US) see a cold snap as falsifying climate change. Another fact is that this is not the case. Climate change, aka global warming, does not say that winter will vanish. (Okay, some alarmists do say that. You need to ignore them, along with the deniers.) The natural variations in winter weather in temperate climates is huge. Climate change has not overcome these huge swings. We will continue to see cold snaps. 


  Are they providing an even and science-based account of the relationship between natural disaster and global warming, honestly explaining how global warming is a complex phenomenon which may have surprisingly different --- and sometimes maybe “counter-intuitive” for lay people --- impacts here and there (including cooling and increased likelihood of sever weather in some areas)?


This depends very much on where one gets ones news on climate change issues. Fox News? The odds are against it. According to one study, 72% of Fox News's reporting on climate change was inaccurate or downright false, with the inaccuracies veering toward denialism. This same study found MSNBC to do a much better job, with only 8% of its reporting on climate change being inaccurate or downright false (with the inaccuracies here being mostly overly alarmist).

That said, an 8% error rate is nothing to write home about, and the superficial nature of the reporting is even less to write home about. The news media is not where you should go if you want good reporting on climate change, or on science and technology in general. I have a rather low regard for news media journalism regarding science and technology. The reporting is rather awful. Keep in mind: Journalists in general avoided STEM classes from the ninth grade and up, and when they couldn't, they took classes like Physics for Poets.