When are IVs, natures, and personality determined for eggs and roamers?

My opinion is that we alreadyhavewaytoomanyquestionsaboutthistopic, some of which have answers that work for 1 or 2 generations, so I want to get the answer for every variable and every generation in one place. For eggs, are they determined when the day care person finds the egg, when the player receives it, or determinedlike this? For roamers, are they determined when it starts roaming, when the player encounters it for the first time, or at the start of each encounter? Can the player re-roll the variables by defeating the roamer and then defeating the champion? Are different variables determined at different times, ie. is it true that in some generations, personality is determined when the day care person finds the egg, and IVs are determined when the player receives it?

Stuff I think I already know:when natures and personality are determined for eggs in every generationsourcesourcewhen IVs are determined for roamers in Crystalsourcewhen IVs and natures are determined for roamers in Generation 4sourcehow swap breeding works in Generation 7source

Please don’t question my curiosity.

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