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.
Yes, this tradition exists (existed?) among the Therevada as well:
The Petavatthu is a Theravada Buddhist scripture, .... It is composed of 51 verse narratives describing specifically how the effects of bad acts can lead to rebirth into the unhappy world of petas (ghosts) in the doctrine of karma.[1] It gives prominence to the doctrine that giving alms to monks may benefit the ghosts of one's relatives
http://en.wikipedia.org/wiki/Petavatthu
They stand outside our dwellings, at our windows, at the corners of our streets; they stand at our doors, revisiting their old homes. When abundant food and drink is set before them, by reason of the past sins of these departed ones, their friends on earth remember them not. Yet do such of their kinsmen as are merciful bestow upon them at due seasons food and drink, pure, sweet and suitable. Let this be done for your departed friends, let them be satisfied. Then, gathering together here, the assembled spirits of out kinsmen rejoice greatly in a plentiful repast. “Long,” they say, “may our kinsmen live through whom we have received these things: to us offerings are made and the givers are not without reward” for in the land of the dead there is no husbandry, no keeping of flocks, no commerce ad with us, no trafficking for gold: the departed live in that world by what they receive in this. As water fallen upon a height descends into the valley, so surely do alms bestowed by men benefit the dead. As the brimming rivers fill the ocean, so do alms bestowed by men benefit the dead. Let a man consider thus—” Such a one gave me this gift, such a one wrought me this good deed; they were my kinsmen, my friends, my associates.” Then let him give alms to the dead, mindful of past benefits. For weeping and sorrow and all manner of lamentation are of no avail, if their relatives stand thus sorrowing it benefits not the dead. But this charity bestowed by you, well secured in the priesthood, if it long bless the dead, then does it benefit them indeed. And the fulfillment of this duty to relatives to the dead is a great service rendered, to the priests a great strength given, by you no small merit acquired (Petavatthu, Khuddaka pátha XII-XIII, trans. R.C. Childers)
A simple and direct answer is, 'Buddhism accepts the existence of ghosts and demons.' They are born as ghosts or demons because of their karma. Some demons are very powerful; they can even kill humans. They are powerful because of the good karma they accumulated in their early lives. However, if they use this power in a negative way, they will accumulate sins once again. i heard some ghost/demon capable eat emotion as their meal. they strong when they absorb theses emotions.
