The first is whether or not the murderer should know who they are. If they do, there's a risk that the game turns into Mafia, with an emphasis on dealing with deception rather than assessing evidence. ... [If they don't] there would seem to be little point in keeping secrets [and] ... some sort of time pressure needs to be introduced.

Spot on, all all counts. There are other ideas that just got posted that might help with this; if players had a limited number of chips and were playing to maximize their chip count, then sharing info would only make sense if you thought it would give you a relative advantage. If the murderer was given weak evidence that he/she was the murderer, that might create a bit of deception without encouraging a Mafia dynamic. Accusations could be made expensive relative to other activities (i.e., you have to go to the Control Room, or gather everybody together, etc.).

Under what circumstances are players allowed to ask each other questions, and is this done in public or in private?

I had imagined that you can talk whenever your characters are in the same room, but you can't ever physically flip over your clue cards to show people what they say. E.g. if you did an autopsy on the left leg and it revealed lead-pipe-impacts, you could say "It was a lead pipe, I swear!" but you couldn't actually give the person your "lead-pipe-impact" card. Just like in real life, we don't have provably-secure mind-bridges. You could, however, give the person the left leg, and then they could do their own autopsy.

There's a risk that the randomisation aspect become sufficiently complicated that it would really need to be done by computer.

I agree, and I'll find ways to avoid that risk. It happens to be one of my talents.

This could be a fun and educational game. Possibly even commerically exploitable.

Thank you! I'm glad you think so.