I haven't used Proshow Producer in years but I believe you can just publish the video directly to Facebook. It asks for you Facebook login information and then it will render and upload the file to Facebook in the appropriate format. It is the easiest way to make sure you render a video in a Facebook suitable format.
You should be able to publish a video to disk and the app should be able to render a mov or avi file. I have not had much success trying to email a video file unless it is very short or I reduce the quality significantly. I usually use some type of sharing service to share the file. You can use OneDrive, iCloud Drive, DropBox, Google Drive or something like that or use a service like SmugMug, Google Photos, or something specifically designed to share photos and video. Some email accounts limit attachment size which might prevent it being emailed.