What is the ruling on designing and drawing animate beings, and does the ruling on drawing them on paper differ from drawing them on a computer?

The correct view is that the drawn image is forbidden, just like the sculpted image, due to the generality of the evidence. Some of the Salaf went to the extent of saying that what is forbidden is that which has a shadow (a physical body), and that which has no shadow is permissible to acquire absolutely. This is a false view, because the image on the curtain that the Prophet, peace and blessings be upon him, disapproved of had no shadow (it was flat), yet he still ordered its removal.