I know that when you record audio in Logic the files are stored in the audio folder in the project. But where are the MIDI files that you record stored?
One thing I do is save my MIDI regions (with instrument and effects on the channel strip) as Green Apple Loops. This way Logic saves it as a MIDI region and an audio file. You can find the audio file in your user Apple loops folder and can easily preview the apple loop in the Apple Loops Library in Logic or Garageband. Dragging a Green Apple Loop to a software instrument track gives you the saved channel strip setting and the MIDI region