Option 1: If you just want to share images from here, just click the little FB button on the image page here and share the image to your own page or to "a page you manage" for your fanpage. This is a one at a time operation and will post each image to the newsfeed, although the way FB works all your followers won't see all your shares. You could just share one a day or a few a week if you wanted to spread it out. Sharing or "liking" an image from FAA will not add the image to your photos on the left sidebar.
Option 2: If you want to add images directly to your Facebook page, go to facebook, go to photos, click on "add photo", or create an album and add your older works there. You can hold down the "CTRL" button and upload a bunch of JPGs at once, (you'll have to create small size images and upload from your computer, less than 150k works best on Facebook) then Facebook will let you rename/edit each one if you like to before you post them. You can then add a link to the FAA page for each image by cutting and pasting the URL from FAA and adding it to the image description. This method definitely adds the photos to your left sidebar on Facebook.
Option 1 will notify your followers about each new image, Option 2 will notify them once that you've uploaded new photos or a new album.