Did you bring the audio into STP using "send to" in FCP? If you did, when you save the file, the FCP timeline should show the STP audio clip in the timeline, replacing the audio you sent. If you didn't use that function or if that's not working, do a save or save as for the audio file project, then you can bring that file into FCP.
You can't export audiofile projects, only save them or save them as another format. You export multitrack projects to for a mixdown audio file.
Conform project is for when there are video changes, and you need to compare the timing of the original to the new video edit to sync up the audio. This function is for multitrack projects.
Hope this helps!