In a casual sense, if, for example, wind didn't exist, wind didn't blow my hair, wind didn't swing anything, wind didn't come into any place, etc. Likewise, I think if something doesn't exist, it doesn't hit my bone, it doesn't dry my tear, it doesn't move, etc.
Is there a theory that says if something doesn't exist, it doesn't do anything, so, that is, existence is prerequisite to do something or have qualities?
Related source: What condition(s) must be met to claim that something exists?
The concept of actuality, in comparison/contrast with potentiality and inactuality, originally involved such a thesis. I think the following search result is an attribution of this thesis to Aquinas, following Aristotle:
The general search for {"to be is to do" "actuality"} shows at least joking attributions of the sentiment to Socrates, but here's another serious result:
Note that the arcane description of God as the actus purus is ambiguous, from a modern perspective, between "pure act" and "pure actuality." But the disambiguation can then be a merger: to be dynamically impassible can mean to be completely existent, to be existence-as-active. (So Aquinas also spoke of God as ipsum esse.)
You are asking questions about the word 'exist' which presuppose it has a single clear-cut meaning- it doesn't. The word can be applied in different ways, and you will get into all kinds of muddles if you confuse them.
Objects that physically exist, in the way that wind, apples, electricity, fork-lift trucks etc exist, can have physical effects. An imaginary fork-lift truck cannot lift a real barrel of molasses. So yes, to exist in a physical sense means to have the potential to cause physical effects.
Imagined objects, or ideas generally, can have physical effects. Consider the impact that the idea of god has had on humanity, for example. However, you need to unpack that carefully. You might consider, for example, that the idea of god is just something we associate with a particular configuration state of the particles that comprise our brains, ie something that physically exists, so the physical effects that the idea of god has on people has, in that sense, a physical cause. You might take the same view of other non-material causes of physical effects in humans, such as doubt, optimism, an imagined ghost, etc etc.
To exist means to have an observable effect on reality.
Physical existence is obviously observable. Physical objects or events can be observed, measured and analyzed.
Abstract immaterial ideas are also observable in the behaviour of people who hold them. Santa Claus does not have a physical existence, he only exists as an idea that has an effect on people's behaviour.
Ignoring causality for a moment (as we are not necessarily talking of objects which vary in time), I think that your question is reversed. Instead, consider that the logical properties which are assigned to a non-existent object are the justification for its non-existence; the object doesn't exist because it was assumed to have certain properties, and those properties are logically impossible to fulfill.
This is usually generalized into the concept of self-defeating objects, as summarized in Tao 2009. No self-defeating object exists, but there is more than one collection of self-defeating properties; these objects would be distinct if they existed, and we can suppose their distinctness in non-existence as well.
You ask:
Is there a theory that says if something doesn't exist, it doesn't do anything, so, that is, existence is prerequisite to do something or have qualities?
This depends on your definition of existence, which is the heart of the undying controversy that pervades ontology. Meinong, Carnap, and Quine, for instance, had different takes on existence. So until you put forth a theory of existence (a metaontological theory), you'll find your answer open to attack from anyone who doesn't think like you. That being said...
Unicorns don't exist, but they do cast magic spells and use their horns to teleport. So, there is at least one form of existence where things don't really exist, but do do things: fictional existence (SEP). Thus, it's not unreasonable to say that unicorns don't exist, but they do magic, weigh upon the earth, drink water, etc. These are the sorts of convolutions of logic that make it necessary to define existence.
Generally, however, metaphysical realism (SEP) does require existent things to have properties of some sort. According to Alexander Miller in that article, there is a criterion for existence:
Generic Realism: a, b, and c and so on exist, and the fact that they exist and have properties such as F-ness, G-ness, and H-ness is (apart from mundane empirical dependencies of the sort sometimes encountered in everyday life) independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on. (emphasis mine)
Thus, under this term of "generic realism", two criteria present themselves: first, things that exist have properties; second, those properties are independent of any agent and their thought. In fact, George Hume created a bit of a stir by insisting that objects are nothing more than bundles of properties. Thus, a modern ontologist must go beyond the criterion set out by general realism, and define what objects are (SEP).
