Cloud Endpoints currently runs on GAE Standard Gen 1 and GAE Flex. We're investigating a solution for GAE Standard Gen 2 (which go 1.11 is, along with python 3.7, node 8, etc.) and GCF.
As for EAP: unfortunately not. Personally, I'd like to see a managed version as opposed to the current framework or sidecar approach, as it'll be easier to implement across products, but that means it'll likely take a little longer.
Any ETA for Gen 2 or alpha signup?