Is there a cache-busting feature?

Yes! See URL Expiry (cache busting).

Relative URLs in my CSS code break if the merged asset is written to a different location than the source files. How do I fix this?

Use the builtin cssrewrite filter which will transparently fix url() instructions in CSS files on the fly.

I am using a CSS compiler and I need its filter to apply even in debug mode!

See CSS compilers for how this is best done.

Is Google App Engine supported?

Yes. Due to the way Google App Engine works (static files are stored on separate servers), you need to build your assets locally, possibly using one of the management commands provided for your preferred framework, and then deploy them.

In production mode, you need to disable the Environment.auto_build setting.

For URL expiry functionality, you need to use a manifest that holds version information. See URL Expiry (cache busting).

There is a barebone Google App Engine example in the examples/appengine/ folder.