To go with your Arctic tern example, just because one bird can dive deeper doesn't guarantee it's survival. It might still get eaten by a predator or catch a disease or just have a run of bad luck that causes it to starve. However, the birds that can't dive as deeply run the same risks (assuming there's no additional risk to diving deeply) and, over a long time and with a large population of birds, those that can dive deeper will survive to breed more often, until eventually the whole population carries that trait.
Because a tendency to hibernate is likely negative for survivorship when it's not necessary - if lots of other animals are moving around and you aren't, then something is more likely to come and kill you.
On the other hand, lots of animals have other varying traits that aren't obviously useful, but don't exact a significant enough toll to cause them to disappear.
> But why would you already have the ability to hibernate efficiently if you don't need it
Doesn't that assume that bears were transported into Canada and survived because they could hibernate? Isn't it perfectly possible that they moved further north gradually, increasing their tendency to sleep in cold conditions as they did so?
Imagine there's a life and death surprise test on evolution. Demonstrate knowledge and you live. Fail to do so and you die. Part of the population already has a reasonable understanding of it. Others don't. You're looking at it from the perspective of the less knowledgeable cramming their study to pass the test. Evolution in this contrived case can select for those who already happen to understand the topic.
Incorrect - it's both. Obviously adaptivity to rapid changes is key, but species don't only disappear/change due to extinction-level immediate events. Individuals also get edged out by their peers (or members of other species) who manage to outcompete them just that little bit for food, or sexual attractiveness, or any of many other reasons.