The construction time for each, assinging it was done on an Anri, is likely a few days to a week assuming all materials are readily available, due to the large amount of standardization between these blocks. If materials have to be synthesized, it can take notably longer. An Anri can make and hold a maximum of four at any given time.
Edit: Ah, you mean the connections for the highways. I must admit that was an oversight. Thanks for catching that one! I've addded some basic gravity control systems to keep that collapse from happening.
This would then require more Anris be built, or that the City Blocks be built by Star Fortresses in some cases. It is also possible, I suppose, to dock an Ayame Layer to a ship with fabrication abilities and materials to produce one.
The city blocks can be used as needed, but are intended more for colonizing worlds we already have. It's part of a public works program Yaichiro plans to propose to the Yamataian government. The UOC will also have the City Block to cater to their needs.
No, it is by no means cheaper than a conventional method. However; since it is largely made out of Yamataium and can resist/repair wear and tear over geological time scales, its utilities are far easier to control and repair than buried utilities, are energy independent, and have various other benefits described in the wiki; these city blocks are meant to last FAR longer than conventional ones. In the long run, it's worth the investment.
It is also an effort to apply the manufacturing and regulation techniques and technologies learned in starship design over the past several decades of combat into a peacetime public project.