2nd Gen Two Questions

So, the game I am currently playing is Pokemon Silver for the 3DS. I have two questions.
1, Am I capable of catching Mew or Mewtwo?
2. Is the capture rate myth true? There is always a 50% capture rate no matter what ball we use except for the master ball?

1. You can catch Mewtwo in the Cerulean Cave but you can't catch Mew.

2. From my experience, the capture rate is 50%.

iirc Mewtwo is only catchable in HG/SS and not the original G/S, for whatever reason

You can't catch Mew or Mewtwo in GSC

dunno about the second question, doesn't seem true

Darn. That sucks.

As others have said, there's no Mew or Mewtwo in GSC, so you'll have to trade one from RBY (Mewtwo through normal means, Mew via glitch). Technically, you can complete your Pokedex through the Celebi egg glitch (https://bulbapedia.bulbagarden.net/wiki/Celebi_Egg_glitch), but it's complicated and isn't the intended way of getting those Pokemon in gen II.

Some of the catch rate calculations work a little strangely in gen II, but no, you don't have a 50% chance of catching a Pokemon regardless of the ball. See https://www.dragonflycave.com/mechanics/gen-ii-capturing for a pretty good explanation of how the catch rates work in gen II, and some of the wonkiness of it. They also have a catch rate calculator you can use to get a better sense of what's going on with catch rates in particular situations.