1) You cannot say that a city is sustainable, but you can measure if some efforts are made to improve the sustainability of a city.
2) Regarding transport, an interesting indicator is the share of active mode for journey to work. The share of transit is important as well. A synthetic indicator would be the evolution of the modal share of cars for journey to work.
3) Regarding equity, there are different measure of accessibility (see Levinson et a. 2017, the book available on the University of Sydney web site)
4) The evolution of economic efficiency or efficacity is difficult to measure. I would tend to measure the usual indicators on a territory clearly associated to an important city.
5) For environmental questions, I would tend to measure the evolution of the expenditures on a city.
Well for question 1 I suggest using the 17 Sustainable Development Goals that can work as a good framework to examine sustainability.
For question 2, I think there are many cities around the world how can fit in this definition; for what is my understanding, Copenhagen is a good example. Question 3 is very general and I'd like to say that the factor is secondary; cities are cities because they are urban contexts but communities are everywhere in both rural and urban contexts and there are many cases of sustainable communities in non-urban settings. I suggest to you this paper Article Renewing the City through Public Participation and Cultural ...
The rapid growth of cities—a result of rising populations and increasing migration—has led to a boom in mega-cities, especially in the developing world, and slums are becoming a more significant feature of urban life.
Making cities sustainable means creating career and business opportunities, safe and affordable housing, and building resilient societies and economies. It involves investment in public transport, creating green public spaces, and improving urban planning and management in participatory and inclusive ways.
"The term sustainability has become like a rubber band that can be stretched almost at will in any direction." by Herbert Girardet.
A city is a complex system and is not easy to define sustainable aspects of a city. As cities are anthropocentric and are our(human) ecosystems, I believe, a sustainable life style is what we need, a community or a city needs. Now its is upto your interest to focus on any particular aspect of a city and define a sustainable approach in that particular dimension. what ever the urban activity may be, an approach that addresses the social, environmental and economic issues and draws an effective plan for a better tomorrow