1) is it designed for / possible to expose non-HTTP[s] backend service using Apigee APIs and proxies?
Apigee Edge platform is lot more than exposing a simple proxy. As you said, it can be non-HTTP(s) like SOAP etc or even HTTP(S) APIs. We call it as an Intelligent API Platform. Apigee deals with entire digital value chain.
Apigee Edge consists of three Main Services,
API Services:
API Gateway, Build Proxies, Add Logic, Secure, Cache, Scale, Traffic Managment , Mediation etc.
Out of the box 30 policies, Extensions using which you can add security, traffic management, message transformation to your APIs.