Pokemon-go – Will changing the Buddy Pokemon reset it’s Total Kilometer walked distance

Anytime the "loading" symbol appears in the corner, your distance is usually not being counted. If you wait for the game to finish loading before you walk, your distance will almost always count. The update is dependent on whether it is able to get a good GPS signal but even if you have excellent signal, if the game is loading it will not update until it has finished loading. At least, according to a number of experiments done by a few people that seem to show that distance is not counted while the game is loading. This would explain the jumps you experience as well, I would think. Hope this helps.

The distance "from the screen" of Pokémon you're catching when you have the AR off has no relation to the max CP or catch rate of these Pokémon. It's just a way to simulate having AR turned on by forcing you to change your throw based on what you're catching.

A prime example of a Pokémon who is extremely close to the screen but does not have a comparable catch rate to other Pokémon that appear extremely close (Caterpie, Weedle, etc.) is Ursaring.

In general, easier-to-catch Pokémon appear closer, but as seen with Ursaring, this is simply a pattern and by no means a rule.