1. Unfortunately, the way that Refried Paper is coded means that to put a border around an icon means a border is automatically put around everything - but there's a manual workaround, even if it's a bit clunky!
Every time you link to an image, use the code <img src="YOUR URL HERE" style="border: none;">
Alternatively, you could just turn off borders on everything by changing the border: 1px in the following part of the code to border: 0px