I’m looking for an instructor station where I can cause things like hot starts and hung starts on turboprop planes like the Cessna Caravan. I don’t even know if FS2020’s Caravan is modeled detailed enough for something like that.
Currently it isn’t. Some third party planes (Kodiak, Milviz PC-6) are as far as I know, but no idea whether you can influence these variables (turbine temperature, etc) to set of a hot start.
You can reproduce failures on most systems live. You can also place aircraft on approaches, change weather, etc. There´s no need of an instructor figure itself as you can use the commands yourself as a player, but it supports it also while working on a LAN if I´m not wrong.
Not sure if this has what you are looking for but worth a look at the engine failures page. You could always ask the author to consider adding the elements you are after.
If you just wanted failures, I would say its price is a little steep, but it seems to do so much more than that.
With the right external software you could hand roll something approaching it with a Streamdeck, along with a free plugin called Flight Tracker, and you could assign a button to disable a system. I could do that with SPAD as well.