Is looking at 3D female characters in video games and in cartoon and anime movies considered a forbidden gaze? And what are the limits of this gaze?

Looking at imaginary pictures is not forbidden, unless they are lewd and lead to temptation (fitna). In that case, it is not permissible to look at them as a preventative measure (sadd al-dhari'a), because the ruling on looking is connected to temptation and lust. Anything that leads to them makes it impermissible to look at.