It is something you do that you are not sure about the outcome. Another word would be gamble or risk.
They mean the same thing because fat chance is sarcastic. The "fat chance" is said, it really means little chance or "slim chance."
An outside chance
little or no chance of success.
It means the same as "to have a chance."
It means completely by chance.
They don't (quite) mean the same thing, the expression:'fat chance' means there is no chance,'slim chance' means that it will be difficult but there is just a chance.
question is,are you willing to give that chance?
by any chance
Assuming that you mean "bonne chance" it simply means "good luck" in French
Give peace a chance
"Bonne chance" means "Good luck".
If you mean the chance of succes, like fortune, it will be, ironically, 'chance'