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?
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.
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.)
