The only thing that 'resets' is the 'daily, weekly and monthly filtering on the Leaderboards. That is at midnight PST (or PDT in the summer)
All other timing is specific to you, when you get an energy tick update (every 2.5 minutes for me), when quests become repeatable again (20 hours or any number of days + 20 hours for some). The house voting ranking updates something like every 5 minutes. Your friends status update every 5 minutes (and guess what, about 99.9999999% of the time that absolutely does not matter but it still happens EVERY 5 minutes and freezes your game for a few seconds).
The other thing to know about the regular rankings/leaderboards is that they are delayed by something like up to 15 minutes. So you can't whack a bush and see your number of bushes incrememt instantly.

If you are trying to understand your score then you have to not look at the ranking for 15 minutes since your last action.

A friend can get help 20 hours after he last got help for that specific thing (energy, gates, house additions...), that help might have been by you or by someone else.
The daily loyalty spin is a very specific time for you. It's exactly 24 hours from the very first time you did the daily spin, or if you missed a day and get reset to 0 it's exactly 24 hours after whatever time you first did it again.
Mine used to be 4:17pm but mid October I was away 3 days and did the minimum of my facebook stuff, since I was Maxed out and 100% in BW I didn't even do BW at all those 2 days and my daily timer now is 11:48PM (when I got home and did BW after that trip).

Among the Profile is a number for days played.
But it's not necessarily days played. I started playing with several others during Beta testing August of 2010, but my number, 500 now, was something like 12 days short of some people. Because of the infinite time it used to take to load the game I used to keep the game open in one browser tab FOREVER (well 2 weeks straight) so it did not increment my number for any of those days.