PSM warning is typical of a discharged, disconnected or very low battery - there is a "reset" procedure ( can't remember it verbatim - but it's something like centre steering, turn more than 15 deg left, back to centre, turn more than 15 deg right, back to, drive forward 5 meters above 3mph or something like that) - but in reality - a slow drive round the block usually does enough - last time I had to do it - by the time I had reversed of my drive, and moved forward enough to pull up the other side of the road the light went off.
More concerning is the alternator/battery light - if that stays on its because the alternator itself ( or rather the regulator/rectifier black box part) thinks there is a charging problem.
Check the voltage across the battery without the engine running, then start it and check again - you should see around 14v as others have said - if there's no increase between not running and running, then it's not charging so you need to look at alternator or belt.
Original cause of flat battery could be a sign of battery age, or not quite good enough charging, but could also be a sign of something being left on, or not powering down correctly ( have heard of trackers going bad ( 3rd party or Porsche VTS), or the PCM unit etc.) but baby steps - see if its charging, make the lights go out and see if it holds charge.