Is it permissible to post pictures of living beings (whether they are people, children, or adults) on social media, and is it permissible to publish tweets from others that contain pictures of living beings?

The matter of posting photographs of people on websites is a point of disagreement among scholars. It is more cautious to avoid doing so, as there is no Sharia-compliant benefit. There is no harm in re-publishing beneficial and useful tweets that are free from Sharia prohibitions, and credit should be given to their original authors.