Welcome and congrats on your first Alfa. I recently bought my wife a 2001 147 (1.6TS) they're good cars aren't they!
The glowing tail lights on a 156 are connected to the rev counter, the lighting controls all run through the tacho on the '56, not sure if it the same on the '47 so might be worth further investigation. Just checked this doesn't apply to 147, sorry.
Milage / odometer flashing is a CANBUS error. CANBUS is a communcation network that a lot of modern cars run on. Essentially means that all the different modules, from ECUs right down to window switch units, are all coded to the CANUS network and all talk to each other - its a communication line and all units have to be coded, like a membership number, and if one of them doesnt belong to the club the odometer flashes to tell you.
The fix is what is called a proxy-alignment procedure, it recodes all the modules the same and invites everyone to the club again. If you have an ELM diag cable and the correct software (MultiECUScan can do it but you may need the full version, I can't remember).
The bulb blown warning message is probably a poor connection, clean terminals and connections and see if it clears it up.
Brake light issue is probably the brake switch on the pedal, easily solved. check if you can check for a fault code for this, it does generate one but wont put the engine light on.
Reversing light - i assume you've checked the bulb so it will be likely the switch on the gearbox. you should be able to search for more info.
the CODE error is the car not recognising the transponder chip in the key - this is picked up by an arial in the ignition and it isnt unheared of for this arial to break down over time. again a search should give more info and probably how-to fixes.
1999 156 1.8TS Sport Pack 3
2001 166 3.0 V6 24V Super
2003 156 GTA 3.2 V6 24V
2005 156 1.9 JTDM-Jet Sport
2008 159 1.9 JTDM Lusso
1997 GTV 2.0TS Lusso
2001 147 1.6TS Lusso
Last edited by Artermis; 28-06-14 at 20:00.