What is the ruling on calling upon someone whose presence is assumed to request something, and is it considered shirk (polytheism) if one doubts their existence? And what is the ruling on calling out "O servants of Allah" in the desert with the intention of alerting those present or seeking help, and is that considered shirk? And what is the precise criterion for the issue of supplicating the absent, and the difference between "talab" (request) and "nidaa'" (calling out)?

The criterion for polytheistic istighatha (seeking aid/succor) is seeking aid from a creature in a matter that none but Allah is capable of. Calling upon an absent entity is forbidden under two conditions: that the call is literal, not figurative, and that the intent is to request something that none but Allah is capable of. If the call is literal and one seeks from the dead or inanimate objects that which none but Allah is capable of, then that is polytheism (shirk). As for a general call, it is not forbidden. Based on this, what you mentioned in the question is not polytheism.