Not really on the summary of 1,2 and 3, but I've now lost the will to live. System docs quoted above say that 3 can/ may be cleared by EKA. I have been in the 3rd state in the past, for sure (after I had a flat battery and was in a fairly advanced lockout , and cleared it via EKA disarm in the Nano - likewise the 96 GEMS I cleared a couple of months ago. The 2001 Thor clearance i did last week was more a case of stopping it asking for EKA each time the ignition was turned off.
Or if you just mean, how did i upset the security system.... lower the window, lock with the fob, pull the sill button (someone has just smashed the window), pop the hood, remove the battery negative (thief trying to turn the alarm off), press the fob button 5-10 times (desyncs the fob). Reconnecting after this then the car is very upset - according to the dash: Engine disabled. Keycode lockout, press remote or enter EKA. They fob is also now desync'd for good measure, I also looked at what would happen if the fob batteries were removed entirely. I dare say there are even funkier ways of challenging the security system but I'm not looking to blow anything up, mine is a working car.
Whether or not EKA is enabled in BeCM the EKA entry option is always open - indeed if you go in on the nano after tripping the alarm then you can see that imm and eka are flagged enable. After clearing with an EKA code the settings go back to whatever they had been originally.