Hungry ghosts and food offerings to the dead One of the four lowest realms of the 31 planes of existence is the realm of the hungry ghosts or hungry shades or petas or pretas.

These cannot be souls or spirits, because in Buddhism, there is no transmigration of souls.

On this page, it is described as:


  peta yoni — here the beings have deformed bodies and are usually
  consumed by hunger and thirst


In the Janussonin Sutta, the Buddha states that food offerings to the dead cannot reach them if they are reborn in hell, as animal, as human or as devas (heavanly beings). However, food offerings to the dead would reach them or other ancestors who are born as hungry ghosts or petas. Those who offer this, would not go unrewarded for their generosity, according to the sutta. This appears to be the practice described in the Tirokudda Kanda.

Ven. Nanda Mahathera writes here:


  Peta-yoni (pa + ita) lit., departed beings, or those absolutely devoid
  of happiness. They are not disembodied spirits of ghosts. They possess
  deformed physical forms of varying magnitude, generally invisible to
  the naked eye. They have no planes of their own, but live in forests,
  dirty surroundings, etc.


Ven. Ajaan Lee Dhammadharo describes them here as:


  Hungry shades come in all different shapes and sizes — really
  entertaining, the hungry shades. Some of them have heads as big as
  large water jars, but their mouths are just like the eye of a needle:
  that's all, no bigger than the eye of a needle! Some of them have legs
  six yards long, but hands only half a foot. They're amazing to watch,
  just like a cartoon. Some of them have lower lips with no upper lips,
  some of them are missing their lips altogether, with their teeth
  exposed all the time. There are all kinds of hungry shades. Some of
  them have big, bulging eyes, the size of coconuts, others have
  fingernails as long as palm leaves. You really ought to see them. Some
  of them are so fat they can't move, others so thin that they're
  nothing but bones. And sometimes the different groups get into
  battles, biting each other, hitting each other.


Based on all the descriptions above, it sounds to me like hungry ghosts or hungry shades are microorganisms. It also makes sense that when food offerings are made to the dead, they would be consumed by microorganisms.

Questions:


What are the hungry ghosts or hungry shades really?
Could they be microorganisms? Have any Buddhist scholars considered this possibility?
Is offering of food to the dead still practised today?
Is this a recommended practice or is it not recommended? And why? According to this answer, the Buddha neither rejected nor endorsed the practice.
Does the opinion of the different Buddhist schools differ from each other on this?
Interesting question... 


  What are the hungry ghosts or hungry shades really?


Likely no one can really explain in words so to make you understand unless you reach the 4th Dhyana/Jhana and see them yourselves ;). Because only by reaching 4th Dhyana you can have Rddhi/Iddhi (psychic power) - to see other dimensions. Yet unlikely meditator if do complete the 4th Dhyana will go around proclaiming he/she achieved 4th Jhana! Imagine an Arhat/Arahant going around town telling everybody he achieved Arahant-hood?! 

However, some hints from the Sutras/Suttas. Hungry-shades are related to one of the Five Hinderances: Greed. In your quoted Ven. A. L. Dhammadharo's, the summerized characteristic is they can't have the way to consume food even they wanted to. 


heads as big as large water jars, but their mouths are just like the eye of a needle: Can't swallow food
Some of them have legs six yards long, but hands only half a foot: Can't reach food or break their bodies
Some of them have lower lips with no upper lips, some of them are missing their lips altogether, with their teeth exposed all the time: Can't eat/chew food


When one contemplate the Hinderance of Greed: Greed is always unsatisfiable, not because of lack, it's the unsatisfiable-ness, wanting more that we called greed, so even there's plenty, to the greed it still means lack, needs more. This unsatifiable-ness backfires caused actualizing their lack-ness: needle mouth, over-short hands, no lips. When this mental state becomes the dominate it will manifest as a physical form that match such mental state. All forms are the manifestation of corresponding consciousness (consciousness is not really an exact term but can't think up better one yet). Animal form is animal consciousness, human form human consciousness. Beware and condemn those Neo-Buddhism followers those have an apetite for twisting the Dharma/Dhamma and fitting it into their self-invented "self-views". If an animal mental state is a self-view of a human how does the existence of animal realm exist in our world? It's ludicrous for those clever men taking a literal term "mental state" treating like a real Buddhist doctrine.   


  Could they be microorganisms? Have any Buddhist scholars considered this possibility?


That's very insightful. I would agree partly with this. Yes, as far as I know there is one Chinese Buddhist teacher Nan Hui-chin said so. I would say this realm some take it as also include the microorganisms, or, mcgms are in-between realms of animals and Hungry-shades. I think the realms should not be read as rigid territories. Like we say rainbows have 7 colours, but we know we can't really exactly say that is red, that is orange in the rainbow. The realms are like this too. 


  Is offering of food to the dead still practised today?


I think in Asian countries most likely, in occasions, like during Qhingming Festival, but many are cultural traditions, not Buddhist tradition. Monasteries may do this too - but for Hungry-shades, as part of their daily practice of sending merits and blessings to all the sentient beings. In Mahayana Monasteries, they usually also throw 7 grains to the courtyards for the Garudas. Because when the Garuda King converted to the Buddha and promised not to kill, however he mentioned there was a difficulty, for the karmic effect all Garudas must eat Nagas as food, or die. Thus the Buddha promised him from then and to the future his Bhikhus will feed them with the grains, so they wouldn't die even didn't eat Nagas. Just read about this story haven't been bother to find any Sutra/Sutta reference yet, but that's what the monasteries do. Would be interested to know if it also practiced by the Theravada monasteries :).  


  Is this a recommended practice or is it not recommended? And why? According to this answer, the Buddha neither rejected nor endorsed the practice.


Personal opinion, I don't think it should be recommended. The Hungry-shades won't be able to consume the food. Unless it's on a specific day or with specific blessing by an accomplished Buddhist/Bhikhus, Bodhisattva or Buddha. If also included the mcgms, it's bad to the hygiene, and mcgms have their way already in natural environment.  


  Does the opinion of the different Buddhist schools differ from each other on this?


As far as I study, I think the general principles are same but may vary in practice.