Does Allah exist in all life forms like animals, plants or human? (Pervades everywhere?)
The answer depends on which theological school you consult. But the most cogent answer to this intricate question is found in the school of Transcendent Philosophy of the Persian 17th century Shia theosophist/philosopher Mulla Sadra, an unmatched genius of Muslim reasoned thinking and mysticism still not widely known to the world.
Here's the answer based on his ontological principles.
For Allah to be omnipresent he indeed has to exist in everything. But this raises the problem since it would mean that Allah assumes the characteristics of his creation (such as shape and color, etc) if he is to exist in creation. However, this problem is resolved within Mulla Sadra's analysis of the nature of being. Being is a unitary unified perfect whole entity which constitutes everything that is without losing its unity and undividedness. I also write Being in the upper case to highlight it as a unique entity. In this sense, Being is contrasted to quiddity which refers to "whatness" of the existing things. All properties associated with creation such as shape, color, taste, etc as well as the concepts that define things (such as tree, man, Earth) are categorized as qudiddity. Yet Mulla Sadra proved that quiddity itself does in fact have no existence or being of its own. Quiddities are just concepts that we abstract from different manifestations of the single unified reality of Being. What makes this abstraction possible is the fact that man can not comprehend Being itself by his faculties. What we always perceive is only the manifestations of Being that unlike Being itself are limited, confined and imperfect. And concepts of quiddity are actually abstracted from these very limits of manifested Being. And since Being can only be limited by non-being, concepts of quiddity does in fact derive from non-being!
Now contrary to quiddities, Being itself is in utmost perfection and goodness. This is because the essence of being is good. Evil therefore emanates from non-being. Creations as manifested Being are in fact a blend of being and non-being with different extents. And depending on how greater the share of creation from being, the better (more good) they are. This also implies that evil and imperfection emanate from either non-being or some lack of being.
Now if quiddities emanate from limitations of manifested being it means that they in fact emanate from non-being or some lack of being. Likewise properties as a class of quiddity also trace back to non-being. Therefore properties that we perceive as color, shape etc are not actually existing things, but they are only perceptions of different manifestations of Being that represent existence deficit.
With this ontology laid out now we can discuss its significance for the question at hand. Being characterized as above corresponds to Allah. I.e. Being and Allah can be used interchangeably for they are one and the same thing philosophically speaking.
Now we know that Allah exists everywhere and in everything. But since Allah is Being not a quiddity, and since quiddities e.g. properties, emanate from non-being or some lack of being, they can never be attributed to Being or Allah! In other words Being or Allah does not assume such properties as shape and color when it exists in things that apparently posses shape and color. Allah only corresponds to the share that that thing has from His manifestation while staying absolved from every property of the said being that implies imperfection.
That was a very rough explanation of the problem of Divine omnipresence according to Mulla Sadra's ontology of Being. Readers may also have a look at this answer of mine to another theological question to learn more about the effectiveness of Mualla Sadra's philosophy as applied to different theological questions. It also makes for a better understanding of the subtleties of his innovative philosophy.
A Shia view:
From Imam Ridha:
مباينته اياهم مفارقته انيتهم.. و كنهه تفريق بينه و بين خلقه، غیوره تحدید لما سواه
His separation from his creation is the separation of him from their essence... his essence is different (does not conflict with his creation) from his creation. The creation (whatever that is other than him) can bind/limit one another (but not Allah).
So if we are to consider that Allah is in the trees, then that means that if a tree falls on another then it is conflicting with another, it limiting one another.... yet nothing can/should limit Allah...
Or that if Allah is in trees, it means that we are considering a form/shape for him... therefore again limiting him to that form and shape... which is again wrong
You asked for an inquiry which can be considered as FAQ of many Muslims/non-Muslims.
Does Allah exists in all life forms like animals, plants or human?(pervades everywhere?)
As a related and constructive matter, Imam Ali (a.s.) said:
… And He is everywhere, without being in touch with that place(s), and or to be beside that. The science of Allah would be conversant to all beings (creatures) and none of those creatures are not empty from prudence (Tadbir or measurement) and hope of Allah.
Therefore, according the above-mentioned hadith (narration) and also based on many other issues and hadiths it can be declared that Allah cannot have a place. He is actually so beyond having any place. On the other hand, it cannot be rational to mention that " Allah exists in all life forms like animals, plants or human".
For a Coranist interpretation of the question, let us note that 112:1 (Pickthal) tells us that
Say: He is Allah, the One!
Since the chapter does not specify who is being referred to in the third person, it follows that the set of valid Coranic interpretations of this verse is generated by all objects to which one can refer in the third person, and hence the answer to your question from a Coranist perspective is yes.
Furthermore, note (112:4 (Pickthal)) that
And there is none comparable unto Him.
To say that God does not hold a property implies that the property is comparable to Him, since the statement "God does not hold property P" is a function of God, the property P, and the quality of holding (a property), implies a need to compare two objects. Therefore, an answer of "No" to any question of the form "Does God hold property P?" is, from an Analytic Coranic point of view, impossible to attain.