Groot - Marvel Cinematic Universe; Earth-199999
If Groot could speak intelligently he would tell you Groot is no mere wood! The citizens of Planet X, where Groot came from were an advanced starfaring species complete with scientists and a curiosity about life in the Universe. In Guardians of the Galaxy we are never told what happened to the citizens of Planet X, only that Groot is the last survivor of that species.
Groot's physical capacity for transformation, instantaneous growth and incredible durability ensure his survival under adverse conditions. He demonstrates an ability to spontaneously grow flowers, transform into vine-like barriers, and extend his limbs at will.
If Groot is destroyed, it is possible for him to return to full health and size though we are not privy to how long this would take in the MCU.
As to whether more than one Groot could be regrown, Rocket has never tried to grow more than one Groot at a time. We are not sure if it is possible or what the ramifications would be. It is unlikely any other unique "flora collossi" would come into existence from planting fragments of a shattered Groot, otherwise why would Groot's people be extinct? He would seed planets with himself if that were the case.
And like many of Marvel's regenerating life forms, Groot does not appear to need a corresponding amount of matter, i.e. water, minerals or soil to alter his size, shape or density, nor does he need such things while he is growing. Past the point of germination, Groot appears to be able to take everything he needs from the air, itself.
Groot - Canon Marvel Universe - Earth-616
Groot had only one appearance in the Marvel Universe, Tales to Astonish Vol 1, #13, Nov, 1960. He came to Earth to take a small town back to his planet for study. He was invulnerable to small arms and could take over trees and plants, turning them into a makeshift army. He was presumed destroyed when a scientist exposed him to altered termites which were claimed to consume him from the inside. (This was 1960, stranger stories were told.)
- Groot does not make a reappearance in the Marvel Universe until we find him in a prison cell, held by the Kree, in the Conquest, Annihilation - Star Lord Vol. 1, #1 (2007). How he escaped Earth, survived his... infestation, etc, none of those things were revealed.
- What we do learn is that Groot can recover from catastrophic injury in mere minutes! Albeit at a far reduced size... After being killed on his mission to free Hala from the Phalanx, Groot is believed destroyed, only to return to life at a diminiutive six inches. He is in all other ways, still Groot. He begins to grow again once given access to nothing but water (er... saliva) given to him by Rocket.
Later depictions in the Guardian of the Galaxy comics show Groot taking more time to grow after being replanted. In one part of the next volume, Groot was killed, repotted and grew quietly taking approximately a week to return to his normal size.
He is also more like his movie person, lacking any communication skills beyond his trademark I AM GROOT. However his technological capacity is not diminished. He correctly decants the imprisoned guardians from their fluid filled stasis prisons, which is not that curious because Groot has received the finest education from Photonic Knowledge of the Arbor Masters.
He is highly intelligent and has a tremendous grasp of quasi-dimensional super-positional engineering and according to marvel's wiki (Groot's abilities information) Maximus the Mad, Black Bolt's brother, asserted that whenever Groot is saying his trademark "I am Groot!" he has actually been saying any number of things. It is the hardened nature of Groot's larynx that causes people, who are oblivious to the subtle nuances of his speech, to misinterpret him as merely repeating his name.
Groot taking on the Spartax warriors who captured the other Guardians. He had been growing in a pot while the Guardians were captured and thus ignored.