You will wear different suits across the story, both female and male ones.
Is there any currently in the game?
You start as a male, but can later wear Chelia, Lily and Noel as the game is now. Wearing them is tied to quest progress.
Will there be an option where you can ask people with Anti Warg to exchange suits or will it only be done through quests?
Through quests. It would become a nightmare to script otherwise on the engine.
