Pokemon-go – What does the pokeball loading icon indicate

The skill combinations are battle moves. I've only been playing for a couple of days, but the numbers appear to be how much damage each single attack will do. (specifically, when you're in a Gym battle).

Your first Pidgey will do the most damage in combat. The final one will do the least.

The numbers represent the strength. The charging bars mean you have enough energy for your special attack (the second one, with the blue bars next to it.) Tap and hold while in battle to use the special attack.

Yes different types of pokemon are a different "distance" away from your pokeball. Flying pokemon such as zubats require a longer throw while small pokemon such as weedles and caterpies tend to require shorter distances. Other larger ground pokemon tend to be in between these two distances. CP also has some effect on distance where a higher CP weedle is further away than a lower CP weedle.

Also for whatever reason Pidgies and Spearows don't really fly so they can also be really close to the pokeball.

Source: Personal experience