Ah well I don't really feel qualified to answer this since I've never run a mystery/challenge based roleplay ever. I did try to start one up a long time ago, but I sort of cancelled it at the last moment after noticing all the ways in which it could go horribly wrong.
My personal recommendation to you would be to try something simple first.
Don't leap into the GM'ing world with huge ambitious ideas since they're only going to get ruined and crushed by a variety of things, even more so if you haven't got the experience to make things flow.
Personally I'd try my hand at something which doesn't involve problem-solving skills and simply go with a standard RP where you incorporate plot-twists, leading character on with some posts only to logically over-turn everything so that you can get the hang of screwing with people's minds xD
If you're intent on running something around the whole mystery genre though I'd suggest going with something bare bones first. Even if it's as simple that adopts the Cluedo format. Experience is everything!
Self-Insert Characters: It's manageable, but yeah it's a bit hard playing all clueless when you know everything. I think it'd work better if you had a spattering of NPC characters to help control the world, rather than having one prominent NPC who seems to be in the know.
Planning: You don't need to know all the details, but obviously you should know the 'truth' behind the mystery, and what your first 'event' will be before you start. As stated above you can't plan everything, and when you invite multiple variables (players) into the equation, your plans are bound to get ruined anyway.
Dice: There are sites that allow you to do dice rolls and then checkup any previous rolls.
I once did a fantasy combat roleplay where dice were used.
We used a website called "Invisible Castle" which let us roll dice.
Each member was assigned a name they had to enter when rolling "Eg; Rakurai5"
The site came with a search function that'd show all rolls done by 'Rakurai5' so if they rerolled and linked to something other then their initial role it'd show in the search. Obviously this had to be done manually and was a hassle, but it was the only way we could make it work at the time.
Dice overall tend to turn away a lot of players so personally I'd avoid their inclusion for a first RP though.
Timelimits: Not against time-limits as a whole, but keep in mind that life will sometimes get in the way. Others might not be happy waiting around with nothing to do for prolonged periods of time. Everything else regarding this has been stated in the above post.
Restrictive GM'ing: Personally I think it's fun on both ends, but my concerns are with the GM. Being controlling can be a huge strain both time and mentally, and I've seen dozens of GM's disappear forever after they realized just how much of a pain it was. Seriously, if you think it'll be a walk in the park, think again.... and I'm not even talking about mystery/controlling RP's xD
GM'ing Tips:
Jig: "Know your players"
Nothing, and I mean nothing is more important in GM'ing for me.
My interpretation of that is probably a bit different than Jigs but here's an example.
"Lets say you're wanting to start your own business, you've put together your store and have prepared everything you think you'll need to run things. The last thing you need to do is get employee's so you put out an advert and several people swarm to you, wanting to fill a vacant slot. This is where the problem starts.
You've essentially drawn several random people from the streets who have different views, different preferences and different ideas. Some work hard, others are always slacking off. The variables are endless, but the thing is, you can't rely on them. They haven't come to you to make your business succeed, they've come to get paid (fun). So the whole 'lets work together' is a farce. Now you have to manage these conflicting, varying personalities while also maintaining your own business.
If you're really interested in doing a mystery-oriented group I'd suggest you either
1) Make a more generic RP and try mustering up a friendship clique you can rely on.
2) Try to juggle friendship gathering and experience collecting by running a mini-mystery.
3) Join existing mysteries to learn from those that are more experienced, keep a keen eye out for those you'd want to include when you start you own RP.
