Okay, I'm not a historian, but I'm a geologist with an interest in history/archaeology. I have studied geology in that area of the world and toured some of the other subterranean cities in Cappadocia, which is in central Turkey, the same region where this city was recently discovered. I'll give the most in depth discussion I can.

Cappadocia is an excellent place for people to build underground cities because the most of the local rock units are made up of tuff (consolidated volcanic ash). Tuff is soft enough to dig into with simple tools, while still being strong enough to support structures. The whole region is covered in structures that have been carved out of the rock, some are still in use today.

It is thought that the earliest structures were small carved out caves. Some of these caves were expanded into houses, churches, complexes, and then eventually a few became cities. What I'm getting at is that these cities mostly grew organically, not all planned out in the beginning. They are confusing to navigate. Rooms are sometimes awkwardly carved into other rooms with uneven floors. Cave ins could happen when construction was over ambitious. Additionally, access to air was a problem in deep parts of cities. Ventilation tunnels had to be built. Clearly many smaller complexes would be easier to build than a large underground city.

So why would the locals go through all of this trouble to build cities? The main reason was for defense. During times of peace, the locals would be dispersed through the region in smaller complexes and caves. Some people would live in the upper sections of the cities, but it would be far from maximum occupancy. Life would not be very different from other above ground dwellers in the area. Issues of disease, waste, food, and water would be less of an issue during these times.

When invaders approached, people from outlying areas would come to the city and wait until the danger passed. Huge rolling stone discs served as doors that closed off the city from the outside world. The primary occupation in the Cappadocia region was shepherding, so they would bring their livestock with them. This simultaneously provided them with food and allowed them to protect their most valuable possessions.

During an invasion, time would be spent caring for the livestock, worshiping, and of course enlarging the city by carving out more rooms. Most of the construction of these cities likely occurred while the locals were trapped inside waiting for danger to pass. Specialized rooms were made for worship, holding livestock, human occupation, etc.

In some cities, water was available from underground springs. Tuff is porous, so water can work its way through relatively easily. There is also evidence of wine production from specialized winery rooms. Wine production may have helped prevent disease from bad water, but that is just my assumption.

I am unable to help with the issue of human and animal waste. I hope this has been helpful, and that others that are more knowledgeable than me will add and correct my summary as needed.