Does Theravada believe in feeding food to hungry ghosts? Certain Buddhist schools perform rituals to offer food to hungry ghosts. And I've heard and read stories that psychic mediums at the rituals saw hungry ghosts came eating the food. Some also reported that they saw Buddha and Bodhisattas accompany the hungry ghosts.

I really wonder and would like to know if Theravada believes in these.
Theravada tradition believe in the transferring of merit to the deceased in case they are in need of merit. If born in a relm where you can sence and rejoice in the meritorious deeds performed you can gain merit. This does not imply that these beings are fed.

There is a Ancient India and Sri Lankan practice in doing leaving food for the Petas but this doesn't relate much to Buddhism. Ratana Sutta does mention harantia balin. So the Buddha did not reject it but I don't think this should be taken as an endorsement also by the Buddha. Hence this practice is outside Buddhism where Buddhism don't accept or reject the social practice at that time.