Closures. No closure of Kings Road is currently envisaged.
Subsidence. No one can guarantee there will be none, but modern construction methods make it highly unlikely, and there will be legal redress procedures. References to problems on CR1 around Totenham Court Road are misplaced; that site is huge, very complicated, and bears almost no relation to what has been proposed for Kings Road.
Construction work. There will inevitably be some disruption from construction, but it will be limited in time and space.
Development. It would be surprising if no development was to follow the construction of the station, but comparisions with Westfields or Oxford Street ignore the constraints of the RBKC planning charter, which limits planning consent to developments in character with Chelsea. According to Retail Week Proerty with refernce to CR1, the view is that it is not the Crossrail stations themselves that will lead to more retail, but development of office and residential space around the stations.