Do pets gain more base skill exp from higher damage rates?

I've always been curious about this for a while. TBH, I don't know how any of the damage rates for pets work. It's all confusing to me, can anyone share a link detailing about how they work if possible? Thanks.

On another subject, is there any way for pets to gain stamina aside from waiting? For example, does running large distances increase stamina gain, or fighting certain amount of movs? I wonder if stamina regens faster when you're online compared to offline.

 

the damage rate is a bonus multiplier.
normal attacks with a 200 pattern will deal damage using 2x the atk stat. a 300 pattern will use 3x the atk stat.
skills have their own values, like player skills, and the pattern value is added on top. so a skill with a 2x multiplier on a 300 pattern will have total multiplier of 5.
but in addition to damage, it also affects speed. the higher the number, the slower it is executed and the longer is the cooldown period.

stamina recovers over a set time period, just like treasure keys and other things.
feeding the pet adds a set amount of stamina, depending on the food type. life potions completely restore stamina.