Stop the player from moving during a parallel process.

In my game, there is a chat group feature, where you push a button and a parallel process starts with the team chatting each other. The thing is that while the start animation of the chat group (adding some image in order with some time), the player would freely move in the map and maybe start another events. So the question is the one of the title; How can I avoid the player from doing this?

Set it to auto start instead.

By definition parallel process means it runs in the background while other things can be done. That includes moving and opening menus, etc. If you want the player to not be able to do anything at all, you use an autorun, though remember autorun = always runs, and that will be at the cost of other events.