Does Ysanne Isard get to perform a free evade action on a stressed ship? Does she get to produce an evade token?

You may not perform actions - even free actions - when stressed (core rules page 17)

Performing an evade action results in an evade token being placed next to the ship (core rules page 8)

She does allow a ship without the Evade action in its bar to perform the Evade action, but otherwise falls under all the other rules for actions.

Ok thanks for the help. I think I have this game down now.

There are some abilities that assign a token rather than say 'take a blah blah action'. You are allowed to receive a token when stressed. Just watch for the specific word 'action'. Like the others have said, you cannot take any action while stressed (unless you're tycho).