What is the ruling on profile pictures on WhatsApp if they contain living beings such as children and birds, or cartoon drawings?

If the photographic images are of living beings, the preponderant opinion is that they are permissible, provided they are not something forbidden to look at. As for images of cartoon characters, the general rule is that they are forbidden and should not be displayed unless there is a religiously valid benefit, such as in purposeful cartoon games and films for children. Incomplete drawn images (from which a part essential for life has been removed) are exempted from the prohibition, so there is no harm in displaying them.