The basement in my house is below the level of the sewer line. We have a holding tank, float switch and the pump has the equivalent of a garbage grinder ahead of it and this pumps the sewage up to the line from the ground level sewer connection.
How does the sewage in one part of town, which is below the waste treatment center, get pumped into it? Is it “pumped” somehow? Do they wait until the sewage has completely filled the pipes?
In hilly areas there must be all kinds of pumps to get sewage up and down hills. Sounds very, very tricky. How does it work?
Gravity sewers flow into the wetwell of a pump station. Wetwell gets to a certain level, pump(s) turn on, and sewage is pumped via a force main sewer either directly to the wastewater treatment facility, or more commonly to an existing manhole that leads to the WWTF.
An alternative for hills is low pressure sewer. Each service connection to the LP sewer has a wetwell and a grinder pump, which gets sewage into the LP sewer. The upside for the municipality is avoiding construction of a pump station; however, costs for grinder pumps (including operation and maintenance) is shifted to each individual homeowner.
“How does the sewage in one part of town, which is below the waste treatment center, get pumped into it?”
We have pumping plants every few blocks to pump it to the plant. They are usually hidden pretty nicely. You can get a wiff of them sometimes.
I guess this is pretty obvious, but not all areas have municipal sewers. The first house I ever owned, in rural Bakersfield*, had a septic system. The folks who moved in next door didn’t even know that they did too. 
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Not a redundancy.
Although my engineering firm designs sewers and wastewater treatment plants, I have a septic system for my own house. Before I bought the house, I spoke to my town’s Public Works Department to see if there were any plans to extend water or sewer out to my neighborhood. (Primarily because this generally involves tie-in fees for the homeowner.) Anyway, the Town Engineer told me that there was absolutely nothing on the horizon. I’m more than three miles from the nearest hookup.
Anyway, there’s absolutely nothing wrong with a septic system. The only real downside is that they can fail, often with no notice, and getting it operational again can be expensive. (I’m talking about failure of the leaching field.)
Mine only failed once, when I first moved in. Luckily I had a friend who owned a vacuum truck, and was in the septic business. Somehow the digestion process had died, too much of the wrong solids probably. He got it started again and advised me how to care for it. I had no more problems for the many years I lived there. If you treat the tank(s) properly and don’t put too much hard stuff in it, you rarely have to have it pumped. Most everything liquifies and goes out to the leach field.
You do have to have a pretty good sized back yard.