What attributes of a Pokemon can be improved?

When creating a perfect competitive pokemon, some attributes need to be correct on hatch/catch while others can be improved. This generation makes it easier than ever to turn a pokemon into a perfect pokemon.

Lets say I have a pokemon that, because of shininess, sentimental value, or other reasons, I want to use rather than breeding something better. It has the wrong nature, IVs, moves, ability, and just about everything.

What can be improved in game? What cannot be?

The only things that cannot be changed are:

• Any specific IVs that aren't 31, such as wanting 0 speed for Trick Room
• Any moves that are exclusive to special events (which SwSh does not have yet)
• The gender of the pokémon, if relevant to the species
• The pokéball it is stored in
• Anything that relies on the PID (Spinda spots, whether Wurmple evolves into Silcoon or Cascoon, etc.)
• Pure flavour information such as characteristic ("proud of its power", etc), time/location met, real world location (used for vivillon formes), shininess

Everything else can be modified.

• IVs can be maximized to 31 through bottle caps and hyper training (requires level 100)
• Natures can be changed through the new mints
• The ability capsule can change an ability from "slot 1" to "slot 2" and vice versa
• Egg moves can now be transferred to pokemon of the same species through the daycare
• EVs can be reduced by EV reducing berries or reset entirely by an NPC on the Isle of Armor and retrained in the desired stats
• The Isle of Armor DLC includes a way to give or take away from a specific pokemon the ability to Gigantamax
• The Crown Tundra DLC includes a way to give a Pokémon its Hidden Ability (although it cannot revert a Hidden Ability back to a regular one)

It can also be assumed that any Pokémon that could only obtain a certain move in a previous game through a move tutor or something won't be able to pass it across once Home is out, but I'm listing that separately since it's unconfirmed.