i'm not sure what exactly you are referring to, but in most cases your pets' distance doesnt matter, it calculates your distance. edit: if its the passive, then yes, you have to be within that range to proc it, pet distance doesnt matter.
yes, thats a control impairing effect, but there are better skills to proc that, unless you take the cold rune, which i think slows them? thats better to use for proccing the gem.
about your 2nd question, yes, any poison skill can be used for that.