What is the ruling on printing pictures of cats, bears, and humorous, unrealistic birds on children's clothes? Is it sufficient to obscure the eye, mouth, or nose to make it permissible if it was originally forbidden?

If the image has severed limbs that are essential for life (such as the head or half the body), then it is permissible to draw it. Similarly, drawing the head alone is permissible. However, drawing a complete image of animate beings is not permissible, even if it is imaginary. Obscuring the face of an image is akin to severing the head in terms of removing its impermissibility.