Leo the cool lion that's cool
its not
The nickname of "The personification of cool" was given to James Dean.
skywalker
cool man
court
Fifi
brantie
cool bananas
I think a cool nickname for Madlyn would be Maddie, or you could even use Lyn as your nickname. Maddie is a more casual nickname while Lyn is a little more formal, so it depends on what type of nickname you want to have.
Yes, many people call her 'Chezza'. What a cool nickname.
A cool nickname for you would depend on what you prefer. This can be derived from your name, your personality or a relevant event that happened in your life among others.