I have one question that has been bothering me for some time. During marshalling phase after I play a card who has a right to trigger first effect? I have heard that this does not depent on who is the first player but always the other players has a chance to react first. Is this true? How is it in melee?
Well, there are two separate issues here. People just tend to think there is only one.
In the Marshaling phase, once a player has counted gold, all players take turns, starting with the First Player, taking "Marshaling" and "Any Phase" actions. The active player (that just counted gold) has the added privilege of paying gold to play things from their hand. But this is considered a "Marshaling" action, the same as triggering a card effect. So during the Marshaling phase, when you play a card, you are just taking your turn to take an action. That means that the person to your left is the next one with the opportunity to take a "Marshaling" or "Any Phase" action. It has to go all the way around the table before you can do anything else, including playing another card.
That's the first issue. The second issue is Responses. When you play your card, you have to give everyone the chance to Respond to it - even before the player to your left has the next opportunity to take a "Marshaling" or "Any Phase" action. In a Player Action window, the player to the left always has the first opportunity to play a Response, then clockwise around the table. (BTW: In a Framework Action window, where the game "initiates" the action rather than a particular player, the First Player always has the first opportunity to use a Response, then clockwise.)
In either case, when you play a card during Marshaling (because you're the active player), the player to your left has the first opportunity to play a Response, then around the table. After everyone, including you, has played all the Responses they want, it is again the player to your left's chance to take the next "Marshaling" or "Any Phase" action. This goes for 1-on-1 or Multiplayer.
I have a example here: Player A is a First player. He play in his marshalling phase a Grand Master Chain on one of his Maester characters. The Player B has already a Grand Master Chain in play, so he wants to use it to discard a Players A Chain. But the same wants to make the Player A that just marshalled the Chain into the play and claims that he as a First player has a right to do this first. So who has a right to trigger the effect first?
Player A is the First Player, so he is the first player to be Active Player in the Marshaling phase. He counts his gold and the Player Action sequence begins. His first action is to play Grand Maester's Chain. Okay, that's his first action. Before he can take his second action, Player B gets to take his first action, which is to use his own GMC to discard the one Player A just played.
If Player A claims that he, as First Player, has the right to use his GMC first, he is forgetting that players take turns to do one thing at a time in this game. And he used his turn to marshal his GMC. If he plays it, then uses it before anyone else gets a change to do anything, he is taking two actions in a row. He's not allowed to do that unless Player B passes on his action.
It comes down to this: Player A, as First Player, does get the chance to do something first, but he used that chance to play the GMC. Now, it's Player B's turn.