Imagine a world much like Earth, except it is nearly tidally locked to its star, making a complete revolution every few thousand years. The planet is far enough away that there is a band of livable area ~300 hundred miles across. Everything on one side is scorching desert, everything on the other side is ice, and both of these regions are impassable and deadly. I want to avoid vast oceans - let's say no more than 30% of the livable band can be water, and preferably the water is in lakes rather than oceans.
I know that winds are a serious problem for such a planet. It would be very windy and rainy all the time. There would also be no night-time (or true day-time either).
What effect does this have on the flora and fauna of this world? With no night, I imagine we would have no nocturnal hunters. With no seasons, hibernation makes no sense, squirrels won't store nuts away for the winter. But what would replace these, if anything? What sort of animals would thrive?