Maybe the Nano sets BECM to send a mobilise high output to ECU at all times. If not, in theory it should be easy enough to find the relevant ECU pin, measure the triggering voltage and duplicate it, thus bypassing BECM input into the process completely.
See extract from RAVE:
Engine Immobilisation (Diesel)
The electronic engine immobilisation feature fitted to
the diesel engine derivatives is different to the
system fitted to the petrol versions.
The BeCM mobilises the engine by holding the
engine mobilise output high. The output will be low
when the engine is immobilised.
Ish... it isn't quite as simple as that in the end - as the BECM sends a pulsed voltage which 'transmits' the immobiliser code to the engine ECU. when I read up on it ages ago, I seem to remember reading something about the differences in immobilisation strategy - where the GEMS model it transmits the code once, and the GEMS ECU the signals the BECM if it's accepted the code (by turning on the check engine light again). Whereas the diesel models (definitely the 'late' EDC, not 100% sure on the 'Early EDC', and the later Motronic systems the BECM constantly transmits the immobilisation code - which is what would measure as 'high' on a multimeter. I don't think you can just bridge it to 'high/+5v or +12V (depending on what it uses as high) and have it run properly.
As you say, you can get a box to bypass the GEMS immobiliser in the ECU, so it will start/run any time you turn the key. There is a way of making the EDC ECU run without the immobiliser aswell, but it involves reprogramming one of the chips in the EDC ECU itself. On the diesels it's called 'Robust' mode, and can only be set during programming on a brand new ECU (basically it's either programmed with an immobiliser code, or told it doesn't need one - and this isn't changeable with standard diagnostics after initial programming from what I've read).
You could use an oscilloscope on the wire between the BECM and engine ECU and see how it transmits the code (my guess is a 12V square wave pulses at specific intervals that make up the digits of the immobiliser code or something along those lines) and then use something like an arduino or other microcontroller to replicate this.
The immobiliser setting in the Nanocom only turns off the passive part of the immobiliser. This is the bit which includes the 'friendly sync' using the coil around the ignition, but also means that the engine is automatically immobilised if it's been running and the key is removed from the ignition, or after a timeout period. If you don't have a working remote, then it becomes a PITA because normally when you put the key back in the ignition, the BECM pulses the coil, which gets the remote to transmit a mobilisation code to allow starting. If the remote doesn't work, then you need to use the EKA to get it started.
Turning off the passive immobiliser means that it doesn't auto immobilise, and will let you stop engine, take key out, whatever, and then it will automatically send the immobiliser code again when the ignition is turned on - the BECM won't expect a mobilisation code from the fob first.
This doesn't stop the engine from being immobilised when the vehicle is locked/alarmed though, so even with the immobiliser switched 'off' in the BECM - if someone broke it, they couldn't easily hotwire the vehicle and get it started - as the vehicle needs to be unlocked/disarmed before the BECM will transmit the code when the ignition is turned on.
Your alarm problem... It could be an issue with the power/ground feed to the alarm - or it could be the alarm sounder itself that has gone faulty. You could possibly probe the output from the BECM to the alarm sounder to see if it is being triggered by the BECM - also depends if you have the batter backup sounder or if it uses the horn.
I hope that helps...
Marty