Hopping speed heavily depends on whether you use mirror mode or not, unfortunately.
As for protect mage, its mainly so if you get attacked by a mage you might be able to finish off the rest of your bones before you die
The pkers themselves are just hopping to the next / previous world because its quick and easy, OSBot world hopping is frankly dogshit, so shuffle world while good in theory will just result in it failing to hop before the pker hits you (it used to be a shuffle system)
I think fast mode causes this, its a weird OSBot bug and I don't have a fix currently.