>>55729398The Wild Pokémon we see are the ones looking for humans. There are some Wild Battles where you are prevented from using any type of ball. Wild Pokémon Battles are the Pokémon testing your strength.
>why do they have higher catchrates when they have low hp/are paralyzedWhen a ball is used on a Pokémon, its body is turned into an energy-like state. The Pokémon being still makes it easier for the conversion to take place and for the Pokémon's mind to be scanned. The Pokémon isn't shrunk down, still with its normal body inside, fighting to get out or something. Notice how you can't catch a fainted Pokémon. The Beast Ball has a lower catch-rate on non-Ultra Beasts because it has trouble recognizing them as Pokémon.
>what exactly to great/ultra/masterballs do differently from normal pokeballsIt's intentionally kept a mystery what a Pokémon experiences inside their ball, but it's strongly implied to be some sort of simulated environment. It's already canon that Pokémon experience the Box System as some sort of place where they are described as doing things such as talking to other Pokémon, practicing Moves and looking for Items. This explains why each ball has different effects, to convince different kinds of Pokémon. Some balls also may just have better technology. As for the Master Ball, it could be possible that it is the sole exception and outright ignores the Pokémon's feelings. Maybe its 100% Catch Rate is an abstraction for it's simulated environment being so good it has never failed so far, or maybe the Master Ball just doesn't activate at all if it detects a Pokémon is unwilling to stay in but before the conversation starts, preventing it from ever failing.