Does only the stratosphere contains enough air for living things to breathe?

No, the stratosphere does not contain enough air for living things to breathe. Most of the Earth's breathable air is found in the troposphere, the layer of the atmosphere closest to the Earth's surface, where weather occurs and where oxygen is abundant. The stratosphere, while it contains some air, has much lower pressure and oxygen levels, making it inhospitable for life as we know it.