How can I improve catch rates in Pokemon Go?

1) This A+B+Down was always a myth and never had any testing to back it up, it was all anecdotes and stories.

2) Not the way you ask, but there are items you can get at higher levels, specifically Razz Berries, that will calm a Pokemon and make it easier to catch. Also, throwing into the colored ring to get "nice," "great," or "excellent," throw will be slightly more effective. Throwing inside a smaller ring to get "great" or "excellent" throw, the more likely you are to successfully catch.
Additionally, throwing a curveball, where you drag the ball in a circle until it starts spinning before you throw it, will also improve the catch rate. While I don't have an exact amount for the increase, it feels like a rather dramatic increase in catch rate from anecdotal evidence.

Yes. If you hold the pokeball down you'll see a ring on the pokemon go from large to small, if you wait until the ring is as small as possible to throw the ball, you will have a higher chance of catching the pokemon.