Full Invisibility: Invisible Kid can use Stealth. Any line of fire drawn to Invisible Kid is blocked if he has no action tokens.

Shared Invisibility: Give Invisible Kid a free action and choose an adjacent character with the Legion of Super-Heroes keyword. That character can use Stealth until your next turn as long as it is adjacent to Invisible Kid.

If Invisible Kid has no action tokens may friendly characters target him with Perplex or Probability Control?
No. If Invisible Kid has no action tokens, Full Invisibility says that lines of fire draw to him are automatically blocked. There are no exceptions made for friendly characters nor is it turn dependent (like Stealth). If you want to draw line of fire to Invisible Kid for any reason, you need to put a token on him first.