Can I skip screens after catching a pokemon?

Solution 1:

No, you cannot skip these screens. However, you can hold down ok/cancel in order for the text to appear more quickly as it is being "written" in the various screens/dialog boxes. Personally, I just hold down the shoulder button so the text scrolls as fast as possible and spam A or B to bypass the user input needed to move to the next screen/dialog.

As for speeding up feeding candies to Pokemon, the only way to really optimize it is to feed it species-specific candies. Species candy will add 1 AV to all stats, as opposed to say, mighty candy only adding 1 value to attack. Additionally, there's no X/XL mechanism where you need to feed multiple candies at higher levels. Feeding your Onix of any level 1 Onix candy will increase all of it's AV values by 1 up to the 200 value cap.