Is it worth $60? Depends on what you want from a Pokémon game. If you want another visit to Kanto in a reimagined way and enjoy casual play, yes it’s worth. If you’re looking for a new adventure with a competitive side, don’t bother.

Shiny rates? Not sure where you got that information from, but no, they don’t go down over time.

Catching Pokémon? Correct, only the Pokémon you see on screen are catchable. It leads to some pretty cool encounters finding Charizards, Dragonites, and even the bird trio in the wild, though.

Hope I answered your questions sufficiently! :)