Additional update: The inline editor issue was caused by setting
BundleTable.EnableOptimizations = true; in the bundle config. Don't know why this broke the page builder's inline editor (specifically our implementation of ckEditor, simpler widgets were still working) nor do I know if it would break on a release/non-debug build as that should enable optimizations as well. Cause is currently being investigated.
(As only one answer can be selected, see Juraj's answer below for the solution to static images 404ing.)