@PriceChild This one's easy. Rep feed uses actual dates (i.e. April 15 = today), while everything else seems to use 24 hour periods (i.e. 23 hours ago = today). That's why the post and activity feeds say your post on April 13 was yesterday.
By "yesterday" we mean yesterday server-time, which is in UTC. So for example if you're viewing your reputation at 12:05 UTC (8:05 EST, my local time for example), reputation changes that happened even 10 minutes ago are "yesterday" as far as the UTC day goes.
I don't follow the "1 day ago" part...because that particular string is never something we display, perhaps you can elaborate so I can clear that up?
The only difference between activity and reputation is that we show by day, since reputation is capped by day from 00:00:00 UTC to 23:59:59 UTC. Actually rolling days in a perfect event days-ago fashion (relative to now) doesn't make sense there...because you would have no idea where events started/stopped/made up totals with respect to the reputation cap. Because of this we group by UTC days, then show what the user's reputation was comprised of that day.
I hope that clears things up...if not please comment and I'll try again :)