If our atmosphere was much thinner (half as thin as we have now) how would animals and humans evolve? Would we evolve completely different? Would we have a quite barren planet? Let's just say that some major disaster caused this back when the dinosaurs existed. Well something that happened that took half of our atmosphere away from the Earth.
Well, the first effect would of course be for anything that flies, like birds or bats. Half the air density means flying gets much harder. So I'd expect flying animals to be smaller in general, but with larger wings.
If it is only the nitrogen that is less dense, this would probably be the main effect on biology. However, let's assume that the partial pressure of all gases (eps. oxygen and carbon dioxide) is reduced.
We can see that effect by going to the mountains. Note that at the top of Mount Everest the pressure is only 1/3, and the partial pressure of oxygen falls up faster because oxygen is heavier than nitrogen. Only on the very top of Mount Everest (above ca. 8000 meters) the oxygen pressure gets too low. So life at half the pressure definitively would still be possible. However, it would also mean that the "death zone" would be at lesser heights.
One obvious adaption to lower oxygen levels is a higher concentration of haemoglobin /the substance that transports oxygen). Indeed, this effect is why athletes like to train in the mountains, because the human body can do this change already; with half the air pressure as norm, life would have been evolved to have such larger haemoglobin levels by default. Also I can assume that lungs would tend to be larger, just in order to get more oxygen per breath.
Another effect of half the oxygen would be less ozone in the ozone layer, because the ozone there is created from oxygen. That means there would be more UV radiation on the surface of earth, and thus life would have to adapt for that. For example, since black skin colour is an adaptation to strong UV, I can imagine that people would have evolved to be black not only near the equator, but also in the temperate zones.
The next class of gases is greenhouse gases, like CO2. Half the greenhouse gases would, of course, mean colder temperatures. Again, you'll find that in the mountains, and of course also closer to the arctic regions.
So in summary, if you want to see the effect of a thinner atmosphere on life, all you have to do is to look at life in the mountains. The only differences of the thin-air earth would be that this would already be the situation at sea level, and that there would be more UV light.
Well, would the lower amout of air affect the total amount of oxygen? Why is oxygen at an equibreum at the partial pressure it is? If that goes back to normal, but we have less nitrogen, it matters far less than having half as much oxygen.
Does the thinner air make for different climate?
Depends how abruptly we would lose half of the atmosphere. Let's go beyond probable (because what you ask is NOT probable) and have some fun: Let's assume that spaceship manned by oxygen-breathing aliens came along and needed to restore oxygen supplies. And because it was emergency, and there was no intelligent life on our planet, they were allowed to fix it quickly without regards about consequences for local wildlife.
So half of the atmosphere was removed to the spaceship within a week, ship left, and life has to deal with the consequences.
Most of the more complex life on land dies immediately, including plants. Some species adapted to high altitudes are able to move lower (but not plants). Very fast concentration of oxygen in oceans falls (as partial pressure with atmosphere balances out) and complex life in the oceans is hit too. UV damage to DNA on survivors on land increases, and most die off by various cancers (skin cancers are very dangerous) within months. Worst hit are smallest lifeforms - bacteria. Even if that are fastest to adapt, most cannot and die. Land becomes 99% lifeless within few years, because food chains will get disrupted.
Oceans are spared DNA damage but species also need to adapt to changed atmosphere - so big part of more complex life perishes too (my crystal ball becomes more cloudy).
But life does survive, and within few millions of years repopulates land again. First on land would be amphibian animals and plants: water shield will help them survive DNA damage, and that are already adapted to live part of life on land. So getting on land second time would be easier and faster. And there would be some hardy survivors to interact with.