In regard to Robens question one by one, straight, defilement and doubts provoking and possible making nervous, for the gain of faith and encouragement to work on the base:
What are the hungry ghosts or hungry shades really?
Could they be microorganisms?
A being ("mind") not capable to get even small satisfaction, even if food righ in front, not capable to take it. Not able to move from it's place, not able to trade. A famous Vietnamese Monks said once: "People who spend their times in Dhamma-centers without to grasp the Dhamma.
Many being in the internet-realm have actually a mind like a hungry ghost. It's good to dedicate shares to them, if having once made merits befor they came in that state, they might be able to take.
Have any Buddhist scholars considered this possibility?
Scholars consider much. It's good to ask those knowing and seeing and with trust in the Noble Ones. If consdering, are scholars today not the most benefical provider for food for hungry ghost, thinking on the many new articels and consume of their work. They possible make much merits if knowing that and setting the mind to their ancestors and hungry ghosts.
Is offering of food to the dead still practised today?
Sure. Where ever there is still right view, where ever there is gratitude, where ever people know mother and father, where ever people know how seldom to gain a human life, where ever cause and effect, destinations of beings, taught by the Buddha, are known, there no one would eat before not having given a share to those before first. Yet it is also fast disapearing on earth at the same time, like right view, the Tripple Gems, prospering times...
Is this a recommended practice or is it not recommended?
The Buddha all wise recommended gifts to ancestors and spirits, recommend, and will recommend. So his, there good disciples, followers do.
- Maker of gratitute. What ever you have been given, you might be able to use, is a sacrify of those having been here befor you and you might even have receive gifts at the time you have been a hungry ghost, had a mind like one, with patient and compassion, yourself.
- In advanced for one self, esay to fall in that stat, even right next minute. Not having given, no support can be ever expected.
- to be best respected and protected by spirits and ghosts
- there are ghost and family members who can be very envy, disturbing and ill-willed, not getting a share.
According to this answer, the Buddha neither rejected nor endorsed the practice.
This answer is not right, uninformed and colored by modernism and faith in materialism rather into that of what the Buddha and wise recommend and all cultures and elders did till some years.
Even if intended to drive people to more refine merits, it misses the point to be in the mids of hungry ghosts and that there are less being who will even reach human life, having gained one for now, in the next, not to speak about capable for grasping the higher Dhamma, and for those having reached firm confidence, such small generousity and good sample for later generations is not a matter of defilements and stinginess.
Does the opinion of the different Buddhist schools differ from each other on this?
In regard of what can be said as old tradition, wiser, with practice: No. There is no school that can be called within the footsteps of Dhamma of the Buddha, with does not only recomment but also practice. They might differ in practice, rituals, folk explainings, focus, intensity, but not on the root: right view, gratitude and generosity.
The only "tradition" (with it's "monks" and lay peopke) that likes to make a better and wiser copy is modernism, secularism and scholar-hood, modern approaches, but they are not regarded as within the foot-steps of the Dhamma of the Buddha.
Some food for inspirations out of "Googlyana", some word written years ago:
Outside the walls they stand,
& at crossroads.
At door posts they stand,
returning to their old homes.
But when a meal with plentiful food & drink is served,
no one remembers them:
Such is the kamma of living beings.
Thus those who feel sympathy for their dead relatives
give timely donations of proper food & drink
— exquisite, clean —
[thinking:] "May this be for our relatives.
May our relatives be happy!"
And those who have gathered there,
the assembled shades of the relatives,
with appreciation give their blessing
for the plentiful food & drink:
"May our relatives live long
because of whom we have gained [this gift].
We have been honored,
and the donors are not without reward!"
For there [in their realm] there's
no herding of cattle,
no trading with money.
They live on what is given here,
whose time here is done.
As water raining on a hill
flows down to the valley,
even so does what is given here
benefit the dead.
As rivers full of water
fill the ocean full,
even so does what is given here
benefit the dead.
"He gave to me, she acted on my behalf,
they were my relatives, companions, friends":
Offerings should be given for the dead
when one reflects thus
on things done in the past.
For no weeping,
no other lamentation
benefits the dead
whose relatives persist in that way.
But when this offering is given, well-placed in the Sangha,
it works for their long-term benefit
and they profit immediately.
In this way
**the proper duty to relatives has been shown**,
great honor has been done to the dead,
and monks have been given strength:
The merit you've acquired
Tirokudda Kanda: Hungry Shades Outside the Walls
May what ever being able to take this gift of Dhamma, have a satisfying and shareful share. May the Devas tell those not knowing, about the merits done here.
"Nur wenige der Menschen sind es, die, wenn sie als Menschen abscheiden, unter Menschen wiedergeboren werden; viel mehr aber sind es der Menschen, die, wenn sie als Menschen abscheiden, in der Hölle, im tierischen Schoß, in der Gespensterwelt wiedergeboren werden." (S 56, 102 - 104)
"only a view human, when departing form human Existence, are reborn as humans, but many humans, when they departing from human existence, are reborn in hell, in an animal womb, in the realm of hungry shades (petas)
from "What leads to Peta-existence
In regard of what is sharing merits, feel free to look here.
(Note: This is a gift of Dhamma, not meant to be used for commercial purpose or other wordily gains, not meant for making one a favor, but intended to liberation: so given to share without bounds to such tings)