I would concur you should have at least 14v across the battery with the engine running, even if the battery is nearly flat it should come up to around that voltage fairly quickly. Sounds as though you have a faulty alternator.

Sounds very much like the battery needs either a good trickle charge OFF the car then a proper load test doing, or replace it for a known good one before checking the alternator charge rate. Trying to check any electrical fault with a discharged battery is pointless.

I did have a very similar fault last week on a VW Golf. Just over 13 volts at the battery with the engine running despite a new battery being fitted. All seemed to point at the alternator until I carried out a amperage test with an amp clamp and found with the lights, heater blower and rear window loading the system almost 58 amps ????

I checked the fuses on the top of the battery and found the 110 amp wafer fuse protecting the alternator circuit to be blue and burnt but still complete. Upon removing the two 10mm nuts securing it, I found there had been a poor connection that had caused arcing and had actually melted the connection in the fuse box which explained the high amperage/low voltage. As a test I temporarily connected the feed from the alternator directly to the busbar and got a more acceptable but still highish 26 amp reading so the alternator may still be faulty, but until a new fusebox and fuses is fitted I won't know ?

Check the fuses, it may be a cause of the fault ?

Presumably you must be charging the battery from an external source as it certainly wont start the car with 1.5 volts, if you disconnect it does the voltage come up to 12 v pretty quickly, if not your battery is u/s. A fault alternator can be responsible for discharging the battery so I would get that sorted out first.