Thank you for clarification.
I think the points which could be addressed with Sentinel-1 are density and fraction of built-up areas, for example by calculating the dual Wishart classification which divides the pixels into several groups (described here: Crop classification using SENTINEL-1A SLC data). Some of these groups indicate the dominance of double-bounce scattering caused by artificial structures, such as buildings. The same applies for volume scattering as an indicator for urban vegetation (depending on the spatial resolution and the size of the city)
I see little chance to detect socio-economic indicators from Sentinel-1 data alone, maybe linked to ancillary data.