Panicked is a burden card and forces you to pass the first player token to the next player.

I'm a bit confused what happens now in a single player game? When I reveal this card, is my turn immediately ended? And what about my next turn? because all my characters are still exhausted. this would implicate that I will have difficulties to quest and fight this turn. Is this the correct resolution of this card?

The card just passes the first player token, it doesn't end the turn or do anything else. In a solo game, the next player doesn't exist so the first player token stays where it is. You just add 3 to your threat and carry on. In a multiplayer game, you just pass the token to the next player, they formally become the first player, and the turn carries on as normal.

There's even a player card called Follow Me! which moves the first player token. It doesn't signify the end of a round (in a single player or multiplayer game), and the token pass to the next player as per usual once you get to the refresh phase.

It is, however, interesting to see how the Peril keyword would proceed.