Well i do not have city and going to buy in a week or so in used:) and im not much of an expert. but i did experience this moving away issue in my cultus and it went away after alignment and steering adjustment. And may be the city, moving away on motorway is due to the light weight and aerodynamic shape of city as i have read in few forums about this issue. Get the tyres checked as well as told above
Secondly the voice coming from your car, i hope it is not the clutch plate or pressure plate issue.
I have coure and when i start the car, there used to be a car sound coming, usually when the car was cold and it goes away,when the car is hot,and when i used to press the clutch it used to lessen or go away (when cold). Few mechanics saw and they said its just a built in problem of gears in the car but nothing serious.
But your issue can be a little different because due to too much pressing of clutch or after much of kilometers driving, the clutch plate and pressure plate worns out and there is also a bearing in between, and the issues in all this one set (clutch plate, pressure plate and bearing) can cause sound and later can effect the fuel consumption, pick of the car, driving the car etc
How much kilometers your car has done
Get your car checked to avoid any future trouble.