Is it permissible to watch female anime characters, given that they do not resemble reality and do not arouse lust, and do they take the ruling of looking at real women?

The depiction of animate beings is absolutely forbidden, including cartoon drawings, unless the images are lacking features, such as being without a nose or eyes.

There is a difference of opinion regarding the ruling on viewing animated cartoons. The more accurate view is that they are not to be equated with real images. However, it is forbidden to watch animated cartoons in which women appear nude or semi-nude, or which are accompanied by incitement to lust, or that involve the exposure of 'awrah (intimate parts), based on the Almighty's saying: (Tell the believing men to lower their gaze) An-Nur/30, and (Tell the believing women to lower their gaze) An-Nur/31.

As for cartoons that do not involve incitement, and in which the characters are veiled or covered, the more accurate view is their permissibility, provided that they are not provocative and are not accompanied by music.