The OED has a lot of senses of "have", and you can debate which is most relevant, but there are clearly some that relate closely to the examples. It can mean to cause something to happen, or to allow something to happen, or to endure or experience something.
There is the causative sense in the OED "V. To cause to come or become, and related senses."
"28. transitive. With complement expressing an action or state caused by the subject." e.g. (under 28 a) "Mr. Low..arranged to have the rental reappraised every twenty-five years." Examples 4 and 5 are causative.
There is another related sense, which relates less to a direct cause than a factor involved in the action taking place: "29. transitive. With complement expressing an action experienced or undergone by the subject." The OED suggests this is "a weakening of sense 28a, with a semantic shift from the sense of causing an action, to allowing it to happen (to one), to enduring or experiencing it".
Specifically:"29 c. With bare infinitive (formerly also †to-infinitive) or present participle as complement. To experience, endure, or suffer (a person or animal) doing something." Examples include Goldsmith: "We often had the traveller or stranger visit us to taste our gooseberry wine." Or the more modern usage "We can't have him just riding away free in a van." (2013) This matches example 1. "you stand here and have that damn thing pop out at you and you not jump" and arguably "have it be extremely popular" (if it is taken as something you experience rather than actively work towards).
There is a negative sense "29 a. In negative construction, chiefly with will not or would not: not to allow or tolerate." Example: "I won't have your father drinking from his saucer like he does, do you hear me?" This is the same as example 2: "I'm not going to have anybody laugh at you, don't worry." (Here "I'm not going" substitutes for "I will not".)
Ref: "have, v." OED Online, Oxford University Press, December 2021, www.oed.com/view/Entry/84705. Accessed 24 January 2022.