What does the message “Too few services” mean

Of course it would be possible, but if you wanted the exact skyline of Chicago, you would have to get every building asset modded to look like their realistic counterparts. The modding community is so huge for this game that no doubt somebody is probably already working on all that as we speak. As far as terrain goes you can use tools like http://terrain.party to generate "height maps" and import them into Cities: Skylines

Districts don't actually do anything to restrict or direct services. Services will be user for whatever is in their local area, regardless of district boundaries (exceptions for power and water, as you distribute them manually).

Districts are useful for:

• industrial specialisation (agriculture, forestry, etc)
• policy specialisation (education boosts, tax cuts, etc)
• controlling lorries (technically a policy specialisation, by way of the heavy traffic ban, but this is important enough to warrant its own entry!)
• adding personal flavour to your city.

On that basis, the game doesn't care what districts your fire stations and fires are located in, which is why this can happen.

As to why it sends fire engines from a distant station instead of a local one (and thus, how you can prevent it), well... I'm not sure, but here's a few thoughts that may help:

• Are all the engines from the closer stations in use?
• Is that road in the middle, where the fire is, one-way in the up direction? If so this makes it "further away" from the stations on the right that it seems, and would be why it's a greater fire hazard than you might expect. It might also be confusing the distance calculation (and thus the selection of station) - consider moving one of the stations on the right downwards.