Hi there
If I remember correctly, I believe my 600 was partly charged when I got it and only took about 30 mins to charge to full. So I think this is normal and if the red light is now off it should mean it is fully charged now.
As far as I know the adaptor for the 600 is the Sony ACS-5220E which I think is also for the 505 from what I read before I purchased it anyway.
Hope you enjoy your 600