Does not having a personal car mean you have no freedom to travel ?

No.  You can walk, bicycle, skateboard, Uber, bus, train, plane...

It means you have to pick other means of transport, just like having no home means you need other forms of shelter. Traveling is limited by your personal resources, however to get from point to point.

Are you in the USA?  Our Constitution guarantees the right to PURSUE happiness, it doesn't guarantee happiness.  In other words, you are free to work, earn and buy a car.

NO. IT JUST MEANS YOU DON'T HAVE THE FREEDOM TO TRAVEL IN YOUR OWN CAR. You're still free to travel by any other means available. Duhhh.

No. There’s public transportation. You got 2 feet to move you around. There’s a bike you can rent. Zip car to rent to drive around. 

In New York, most people use public transportation to get around because parking is near impossible and there are so many crazy drivers. 

No.  It only means you do not have money to buy one or chose NOT to have one because your city was smart enough to invest in public transportation.  And there is always Uber now.

Not always, it depends what your local public transport is like.