Yes, I use padding on all of my wipes.
The trim is called gimp or scroll braid or french braid. I do get some of my colors from Joanns and hobby lobby. Try Papermart.com though. They have 2 different sizes and sell it by the roll pretty cheap. When using the gimp make sure that before you cut it you either hot glue the back side or use nail polish. This will prevent it from fraying when you cut it.