I think that there is no service returning all classes, properties, individuals, etc. Actually, we try to avoid such services for the fear of returning too much results if the repository is huge. For example, the trees are compute on-the-fly as each node is expanded by the user.
Concerning the UI, I'm not definitely an expert. However, generally speaking, known services are exposed as a Angular services which they can be like a function call. For example, here the client invokes the getNarrowerConcepts service:
Here is the definition of the service:
The implementation of the service internally use an HttpManager, which composes the HTTP request based on the provided arguments, service name, etc.. while adding (on its own) contextual parameters (e.g. the context project) and the service base URI.