I CANNOT figure out how to fix my picture links in this article to save my life! What the heck?

Fixed the image links. The problem was with the space in the file name. A space is not valid in links; a space has to be replaced with %20 to work. As an example: "hello world 007.jpg" would be "hello%20world%20007.jpg". The problem is that browsers these days will change "%20" to a space when they display it in the URL bar at the top, but behind the scenes they know it should be %20.

I also changed images to links since it's not apparent that they're not released under a CC-SA license. You have them linked from your photo album, so I'm made the assumption you're not granting anyone the right to use them under a CC-SA license. If you do want to do that, then you can easily just edit the page and remove the text in the link and it gets automatically converted to an image.

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As an aside: To convert the links to just images... (color coded to show the different sections and how they match up to each other)

This
[www.sugarglider.com/images/icon_image.gif</font id="blue"> Link To Image (link text)]

can be changed to this to make a clickable image
[www.sugarglider.com/images/icon_image.gif</font id="blue">]

or changed to just this to only show an image, not clickable.
www.sugarglider.com/images/icon_image.gif</font id="blue">