They stated that temperatures around the world would exceed 700 degrees Fahrenheit for about a day, the 212 degrees mentioned was during the dramatization while some of the characters were still outside.

Preparations in a years time is easy if you're the only one attempting to do so hence supplies and workers are readily at hand but if the majority of the population are trying to dig in for safety, you've pretty much just have yourself and a shovel to count on. It's amazing how quickly the supply chains break down and how quickly assistance becomes unavailable as we experienced here in Houston during Rita. Where will you get the concrete for your bunker if the concrete company is busy with their bunkers?

As to the recovery of the biosphere, all ecosystems eventually achieve a stable state however the larger the impact of a stressor, the more likely that the stable state would not be the original one, they predicted that the stable state would still be hospitable though bleak based on evidence from prehistoric impacts. Most states available are not so hospitable and often involve periods of oxygen depletion as experienced in that biosphere experiment out in the desert, I believe it was call Earth II or something like that, there the stressor was the introduction of the human occupants and they wound up having to pipe in oxygen to keep the artificial habitat livable. With the comet impact and the weeks of solar deprivation, it would be a matter of whether sufficient plant life in the absence of competition could produce enough oxygen to restore the atmosphere to a breathable state particularly after the day of 700 degree heat where anything combustible worldwide would've burned.

They did say that there are more variety of life in today's earth so the chances of the appropriate species surviving with just the right characteristics to produce a habitable world is much higher than it was during the prehistoric Yucatan impact but it is likely that there may be a period of time where the very air may not be breathable and that period of time could be anywhere from days to centuries. The show was an optimistic model of what could happen after such an impact. In Earth's prehistory there was at least one impact that would've totally annihilated life and that was the one that produced the moon, fortunately it was before life had evolved.

I do wonder about how ineffective the nuke was, I would've expected an offset blast to maximize trajectory deflection rather than a straight on shot and though having a rocket capable of reaching the comet at an optimal point would be near impossible, the strength of the nuke should just be a matter of how much weapons grade material is on hand and how honest the governments are in releasing them for use. I would expect the effort to fail for political and strategic reasons or for lack of a large enough rocket.

The show was obviously Eurocentric as the Ariane V is not the largest rocket, besides I suspect more than one rocket from more than one country would be used, a sequence of offset blasts may have better luck in deflecting the comet, followed by blasts that attempt to pulverize it when it's apparent that it hasn't deflected enough. If there was enough time, some form of mass ejector would be used to use the unique makeup of the comet as propellent, a nuclear reactor used to vaporize bits of the comet to eject through a nozzle would have more of an effect over time than a blast, again this would need an even larger rocket to get there years ahead and the ability to accurately predict the comet to be on a collision course years in advance