To play Pete Says 'You must be completely caught up in the Faded Memories event to participate in the spirit offering goals' does anyone know how I can do this? When was that event?

The event is still going on. There's an active forum for it, including spoilers from all the previous steps to help you out if you don't want to slough through it the hard way, and it's all over the news page. It's the same event that caused your HA to lose its color, after a Random Event you would have gotten some weeks ago about something rushing past you and you feeling tired.

Where do I go to play pete says?

It's here but I don't think it counts for the news page bars anymore, it says they're no longer accepting offerings. [edit]