Per instance settings on blocks with context? Blocks normally have a single global configuration.

What options are there to provide "per instance" settings on blocks, so that I can vary them depending on where they are displayed, when they are handled with Context?
If you use Context module for block positioning - you don't need to make any changes at /admin/structure/block page.

All configuration are done in context /admin/structure/context

If you need to display the same block on different places/pages/regions - just create different context for each condition.