WP-FaceThumb allows your visitors to take a picture with their webcam and post it on a widget to your blog.
Yes, you have to go in the "manage gallery" tab in the WP-FaceThumb settings and you can delete or simply hide the photos.
Login to your blog dashboard, go to 'Appearance' -> 'Widget' and drag and drop WP-FaceThumb from Available Widget to the sidebar you want the plugin appears.
Yes, here is a complete guide about this setting and how to customize it
Don't worry, just check if the photos are set to yes in the visible column and make sure that the moderate function is set to no if you want the photos are automatically shown