APM Application URI (no virtual server) ... how to modify caching, rewrite?

Regarding the caching aspect, you could consider a couple methods. From within the Portal Access resource, at the bottom there are resource items (which are used to allow access and for rewriting). In each of those, you can specify a client cache configuration. The other option would be to check the in an iRule and use the CACHE command to disable/enable caching as desired.

Regarding the rewrite behavior, since the APM is proxying the requests, I would say just set values in the Rewrite List and/or Bypass List in your rewrite profile (you can use * as a wildcard) for hosts that aren't part of the Portal access resources.