It occupies a span of time during which it is capable of interacting with other existents.
By detecting an effect caused by it.
By the absence of expected evidence for its existence. If no evidence is expected, we cannot show that it does not exist, the so-called proving of a negative.
The chair occupies a series of consecutive moments and can be interacted with even if that interaction is only light from its surfaces entering our eyes. To say that Sherlock Holmes and Santa are nonexistent is to say that they cannot be interacted with. We assume that that has always been true when we call them fictional characters.
We can, however, talk about the idea of these two, which do exist, and which came into being when somebody first created their stories. The way we interact with ideas, which exist only in minds capable of apprehending them, is different from the way we interact with entities that reside outside of the mind.
Consider Russell's teapot. It exists or existed (or will exist) if there is a time when it can in principle be experienced.
No. The undetectable even in principle and the nonexistent and are indistinguishable, and can be thought of and treated the same.
Hard questions.