I really hope you do carry on doing this as a series, in answer to all of your questions, I think you should look at what can stay true to the source material first and then look at what you can do to balance it, everything has the power to be balanced with other parts of the game.
mechanics
- should stats be private?
No, but I don't think you should have anything that can abuse this (such as DK's thing)
- should the sender of items be private?
Depends on the item but no (maybe you could include a negative item thats secret)
- should you not receive the identity of your attacker?
Not for a normal attack, reveal those (maybe items/events can change this)
- should you not receive the results of your own actions?
Should always normally know what you've managed to do (but again there could be events/items to change this)
- which dice roll(s) should you see the results of, if any?
Always know the exact die number you roll, like in the game
- should rooms be harder to find or have a different distribution?
I think this is probably one of the biggest things you should change which could help out scum. I'd recommend having a lot more events and a lot less items (I believe the main game has more event rooms than item rooms) and then have some more negative events in the game. With this you can then include the rule that Scum don't have to do events (as per normal rules) but may if they wish. This can help scum because it'll mean that the good team can get hit by random stat losses.
- should actions be unlimited or set to a different threshold?
Whilst I personally quite liked the system you had, it does lead to the obvious problem of leashing night actions, a good way of combating this is to have it as a dice role, start the game with 1 dice roll, if you roll a 0 then you must explore or visit a public room, if you roll anything higher than you have the option of what you wish to do with the number you rolled=the number of actions. And then have rooms/events/items allow for more dice to roll.
Within this system you could say that like how scum don't have to do events, they have a bit more power over their rolls here, maybe a 0 roll for them still gives them the option to do what they want but just 1 action.
- should stats have a different scale/limit?
Eh, I don't think this should be changed, I think this was alright as it is tbh
- do stats need to be easier or harder to change?
I think it should be easier for them to go down maybe?
- were items too overpowered?
A little bit imo, but I think adjusting for events and stuff and if items are rarer then it should be fine.
- should the number of players be adjusted (eg 3v8)?
All depends on the haunt and how much possibility there is for night death, I'd maybe make it 4 scum if there's not gonna be a guaranteed night death
Haunt balance
- were labs too easy to destroy?
No, I think they were fine
- should scum have been able to destroy them in order to prevent confirmability?
I think within the next haunt there shouldn't be too much to confirm anyone
- should the distribution of labs have been higher?
Not sure, I think having roughly 2 around at any one time was a good number
- should the labs have been less difficult to activate?
I think being able to activate them easier could've been helpful for them
- should doctors have had additional factional night actions? what type (ie extra attacks, extra lab activation, extra open actions for whatever they want, or some combination of those)?
I think a haunt involving a monster would probably be the best way to combat this, giving a monster that has unknown stats and maybe a couple of thematic powers could be good. This allows for an anon attack mechanic which has a higher chance of dealing damage (and can't lose stats)
As for randomness, I think it's good to keep in the randomness but as said before I think that scum should be able to avoid some of the elements of randomness (ie through events)