Lots of questions...
1. It doesn't seem to be spelled out in the rules but I would think a prison challenge means that the prisoners are not allowed to leave the prison at all until they are ready to move out after being "rehabilitated".
But as it doesn't appear to be written out (or maybe I missed it)... so can the prisoners go off lot for whatever I want? Or are they not allowed out of the prison at all and thus certain skills won't be possible? Or something in between - like they can go out for skill stuff (eg. fishing) but nothing else?
Probably the name of this challenge is meant to indicate what the answer is but I'd like to be completely clear 
Once sims enter the prison, the warden should lock them inside the prison until their release. No leaving the prison, even to fish.
However, doors might get unlocked while the warden's away arresting a new sim. I play-tested this and the prisoners remained in their cells during the warden's 90-min. absence.
In my multi-gen challenges, though, a sim often returns home to find locked doors unlocked.
If your warden comes back to find their prisoners not where they should be, just send them back to their proper places and check the door locks.
2.
How about the kleptomanic trait - no extra rehabilitation points for this one?
No.
3. If we accidentally lose track of the time and our prisoners aren't locked in their cells by 11 pm, do we fail the challenge immediately?
If the team would like to allow a little leaway for error on this, here's one possible suggestion you could go with... If you accidentally miss the 11pm deadline for locking prisoners in their cells, you can keep going with your challenge but your prisoners have to spend the whole of the next day locked into the cells (no skilling) so that there's no way they can possibly miss the 11pm deadline the next night. Then, 6am on the next morning after they spent the full night in their cells you can go back to the normal schedule. It would be a significant penalty but not quite much as an immediate fail. (Or various other options along these lines.)
The lockup time has been modified to a 10:45-11:15 pm range, followed by 7 consecutive hours of lockup.
A penalty of a 31-hour lockup has been added for missing the lockup time (the usual 7-hour lockup plus 24 additional hours).
4. I don't think I fully understand the rule about the outside yard. Are the prisoners meant to all go outside in the yard together? Or does it mean that if 1 prisoner goes outside for 2hrs, that's it, no other prisoners are allowed outside in the yard on that day? Or...?
Yes, the prisoners all get 2 hours of outside time together each day. It's considered a privilege of sorts.
They'll need to walk through the yard to get to different parts of the prison, but they can only "hang out" there for 2 hours a day.
Due to limited starting funds, your outdoor yard will start out small and empty but you can make it more appealing later.
5. We ignore the $2000 cash requirement for our first arrest, yes? After following the set up instructions we will only have $1000 and the warden is only allowed make money by arresting prisoners.
Yes, that's correct. Your warden has only $1,000 but would already have a cell and shower ready for their first "guest."
6. Selling off skilling items once we no longer need them for our prisoners - allowed or not allowed? I'm not sure whether this would fall under any of the acceptable income categories.
Not allowed. If your prison doesn't have room to place the skilling object on the lot, place it in the prison inventory.
7. Can I build myself a starter prison this week, save it into my library and then place it into my real file once I start the challenge? It would save me time on building next week.
Also, sharing it with others via the gallery - yay or nay? It wouldn't be anything special though.
All players have two options for their starter prison: (1) build their own prison or (2) download/edit the starter prison linked in the first post.
The starter prison provided could be much cheaper for players with additional packs, but I used all base game items out of anticipation of a "Not base game" comment from you, lol.
Please do not upload your starter prison to the Gallery until after the challenge ends.
It's fine, however, for players to build their own starter prison or edit the starter prison provided in advance, then upload it to their MyLibrary for later use.
8. The way I understand it is you have to do 14 unique skills with your first 7 prisoners (2 each) but then after that you only have to make sure that a prisoner's 2 skills are different from the last prisoner to leave. Eg. If prisoner #8 does writing and mixology, prisoner #9 can't do either of these but prisoner #10 can do writing & mixology.
If a prisoner finished unexpectedly early causing an issue with your order, then I guess you have to keep them in the prison until they can leave without breaking the rule..? Ie. With the same example from above, if prisoner #8 has just left and prisoner #10 unexpectedly finishes writing & mixology before #9 is done... then I would assume that #10 still cannot leave until after #9 (or another prisoner with different skills to #8) has been rehabilitated and moved out first. Is this right?
That's correct. In your scenario, Prisoner #10 would have to wait until after the release of another prisoner who's maxed skills other than Writing/Mixology.