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

Question

My opinion is that we already have way too many questions about this topic, 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 determined like 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 generation source source
when IVs are determined for roamers in Crystal source
when IVs and natures are determined for roamers in Generation 4 source
how swap breeding works in Generation 7 source

Please don't question my curiosity.

Comments

I don't know for all the regions, but for Gen 8 Sword and Shield, the egg values (including whether or not it is shiny) are determined when the nursery worker folds her arms to indicate she has an egg. For the roamers, (the Galarian Birds) it is determined when you encounter them, so you can keep resetting and catching till you get the best IVs/Nature that you want. Hope I helped! :D
NOTE: This isn't an answer because you asked for all the generations, and this is just Sword and Shield, but still :)

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I decided to make an answer from the questions you have provided.

For eggs,

> However, once the egg is in your party, everything is pre-determined. Nothing about the Pokemon is determined prior to accepting the egg.

[Sauce][1]

For roamers,

> The IVs for Entei are locked in the first time you encounter Entei in the wild, and likewise for Raikou (but locking one of them in doesn't lock in anything about the other).

[Sauce][2]

And,

> In gen 4, roaming legendary Pokemon's nature and IV's are set upon release into the wild. If their nature and IV's aren't to your liking, you'll need to KO them and beat the Elite Four again to re-release them into the wild to try again. There are no actual roaming legendary Pokemon in gen 6; you can soft reset the birds once they settle in to Sea Spirit's Den.

[Saucey][3] [Sauce][4]

I hope I helped! And didn’t annoy anyone with sauce


  [1]: https://pokemondb.net/pokebase/329605/if-save-before-getting-egg-can-just-soft-reset-until-its-shiny
  [2]: https://pokemondb.net/pokebase/319752/how-to-shiny-hunt-roamers-in-crystal
  [3]: https://pokemondb.net/pokebase/276795/when-are-natures-and-ivs-determined-for-roaming-legendaries
  [4]: https://www.smogon.com/forums/threads/orange-islands-sqsa-thread.3603112/page-14#post-7632793

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The first source contradicts https://i.imgur.com/M7x08pp.png ,  so it's probably wrong. The other 3 sources don't include information about generations 3, 5, and 8.

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Alright, I’ll just hide this.

Edit: ok ill unhide it and just convert to a comment. I forgot that feature existed