Oh well the illumination part is showcased through the character's "headlight," in which it serves as the character's beacon and weapon, since the light beam itself melts/vaporizes enemies.
As for the curvy movement, it was actually surprisingly simple! The game linearly interpolates the character's direction towards the target direction (mouse click) at a rate controlled by a turn_speed.
var new_direction: Vector2 = (target - player.global_position).normalized()
direction = direction.lerp(new_direction, turn_speed * delta)
velocity = direction * speed