Instead of using Agda on a filesystem (with EMACS, terminal, etc.), is it possible to use it directly from Haskell, as a library? For example:
-- UsingAgda.h
Yes, it is possible. Agda was designed as a Haskell library plus a main module.
You can see a couple of small examples here. As a bigger example, I wrote Apia (shameless plug), which uses Agda as a library.
Please keep in mind that the current Agda description says:
Note that the Agda package does not follow the package versioning policy, because it is not intended to be used by third-party packages.
Of course, it could change.