Only if you limit your work and social life to that particular city. Not something most people want to do.
Depends on the public transport network where you live. I used to work with someone who commuted from London to Cambridge (yes, that way around). And in Berlin, someone else who commuted from half way to Poland.
Won't work everywhere, e.g. from what I saw when visiting I don't foresee US cities rapidly integrating enough good public transport to properly replace cars within themselves, and from what I've heard about how municipal organisation works in the US even less so for a convenient and well integrated intercity network, but it can be done.
I don't. Long distance trains exist too, and I can watch a movie or eat at a restaurant car there rather than focus on the road.
You can use public transportation, bikes, car pooling, taxis and rentals for your rare-use needs, and its usually cheaper than owning and operating a vehicle.
I'd say that the vast majority of people who live in a city both work, and socialise almost exclusively there.
There are many places in the world this is not true. I would say about half the people I know who live in London don’t own a car. They travel plenty - probably more than the people I know who don’t live in London. If they really need a car once they get to their destination they will rent one, or use taxis.