What is the central question ethics tries to answer, and at which two levels does it ask it?

"How should we organise our life together so that we can live well?" — asked both of the individual (which virtues should I develop?) and of the community (what makes politics just and the economy good?).

The formulation matters: it is about living together, and about living well — not about obeying rules for their own sake. From that one question, two lines of enquiry fall out:

• At the level of the individual: which characteristics and virtues should a person develop in order to be of use to the common good? This is where virtue ethics lives.
• At the level of the community: questions of politics — above all justice — and questions of a good economy, in the original sense of household management: how needs are met and provision organised.

There is a historical point attached. In traditional societies these questions were normally embedded in a larger frame — religion, tradition, authority — which supplied the answers. Modern, pluralistic societies have no such shared frame, which is precisely why ethics has to be argued rather than simply inherited. The loss of an automatic answer is what creates the need for a method.

Go deeper:

• Wikipedia: Eudaimonia — the »living well« that the guiding question points at, and why it is not the same as feeling good.
• Stanford Encyclopedia: Value Theory — what it means for something to be good at all — the layer underneath every moral theory here.