Hi. We haven't been playing long, but I play a Hocus and for what its worth, here are my answers. :)
1) "Personal share" of barter
I have not discussed this with my MC, but I treat my Hocus's barter as persistent. I wouldn't see why it would not be, and there isn't any indication in the rule that it is not.
2) Fortune roll: beginning of each session, or only when it fits?
Regarding the fortune roll for followers, I'm curious as to why it feels unnatural to you to roll at the beginning of each session?
I'm playing a Hocus currently and (so far) we roll every session. Our sessions have been about a day or so in length, and have followed directly on from one another, so that sounds very similar to what you are describing. And it seems to work from my point of view. When we roll we just spend a little time working out how it fits the fiction and thats it.
Personally I'd be a little annoyed if the fortune roll was changed from "every session" to "whenever it seems to fit" as the fortune thing is a large part of the Hocus character, and one of the reasons I chose that playbook. Changing that to something which might only happen occasionally (subject to the whim of the MC likely) would be a big change to the way my character worked, and not in a way I would like.
There are other moves which are written as being triggered when the fiction fits. But this (and others such as the Hardholders wealth move) are triggered by meta-game timings such as session start/end. I don't really see a reason to switch the Hocus move from one type to the other.
But, these answers are just our game, and I would think that there are plenty of other ways this is dealt with out there :)