I like the idea of bringing in the Icons to a 5E campaign. I think its the one thing in 13th Age I found unique enough to want to steal. Is the mechanical aspect of Icons OGL? If so, it might be nice to include a summary. Keep in mind not everyone will have 13th Age.
On first blush through, other than some basic editing issues, I think this looks decent.
I'm no legal expert, so when I tried to find whether or not the Icons of 13th Age mechanics are OGL or not, I failed. So, erroring on the side of caution, I won't put the rules there.
For my game, I'm not even going to use the die roll mechanic every game. I feel it will dictate too much on how the session goes. Instead, I may ask for a roll if the characters are dealing with somehting in the Icon's purview. I'll go back and re-edit that first paragraph (along with the edits you mentioned) to solidify that idea.