A empty 12V would produce the symptoms that you observed (as andy mentioned).
But only for a few minutes after startup with an empty 12V.
If you can start the Twizy (more precise the DC/DC) with a mostly depleted 12V Battery , it will probably be charged to a sufficient voltage in the next 5-10 Minutes.(had tested this involuntary on a 2012 and 2014 Twizy )
After that, the symptoms should be gone.
Plugging in the Twizy to the grid should also work likewise.
Have you tried to disconnect the 12V for a view seconds? (30 secs and start?)
In very cold weather the BMS sends an alarm to the UCH which sets the symbols you mentioned.
They disappear during driving when the battery reaches 0 degrees C.
But you never get the stop and 3 beeps.
A last thing you could try is to pull the 60V fuses as mentioned in the manual.
After that it gets difficult.
A lot of problems produce that alarm condition.
(speed encoder, malfunctioning engine immobiliser etc.)
We had some cases where the battery connector to the charger got a little leaky in winter and produced such alarms.
But thats something you should let your garage have a look at. The connector is very flimsy and can easily damaged (it is also only rated to 10-15 insertions!)
And obviously the is that nasty 58V wit up to 500A. Nothing you want to experience!
The best thing would to lat the garage read out the alarm via ODB2 or try to get a CANclip(or clone) with software.