On the issue of encounters between long rests, here's one adventuring day for the PCs in my game (started the "day" at 14th level, finished it at 15th level):
*Comp 2 L14 skill challenge (as a result of which each PC lost one encounter power until their next extended rest);
*L17 combat;
*L15 combat;
*L7 combat;
*L13 combat;
*L15 combat;
*Comp 1 L14 skill challenge;
*L16 combat;
*L14 combat;
*L13 combat;
*Comp 1 L15 skill challenge;
*L16 combat (the L15 solo was defeated by being pushed over a bridge down a waterfall);
*L15 combat (the solo returned later in the night, having survived the fall and climbed back up).
That's 9 combats within L-1 to L+2/3; even if you put the last two together as "really" one, it's 8.
Plus a 7th level combat; plus a skill challenge's worth of encounter.
That was maybe the hardest I've pushed the players in the campaign; but it's not wildly out of character for our game.
Another example, where the PCs start the day at 26th level:
* Comp 3 L26 skill challenge;
* A L 32 encounter in stages but with no short rest and with the PCs splitting up, starting with a level 26 element, then a couple of PCs falling down a cliff and having to deal with a level 22 element, and then a third front of a 26th level element which initially was one PC, but then ivnolved the other PCs arriving to help him out, plus some other odds and sods;
* A level 27 encounter that, in play, was very hard for party level +1;
* The PCs reach 27th;
* A level 31 combat, surprisingly easy compared to the level 27 one;
* A level 29 combat;
* A level 26 solo combat, involving a couple of significant crits, including one with a fighter daily that limits the target to basic attack, which is terrible against a solo;
* A level 27 combat encounter;
* A level 27 complexity 3 skill challenge;
* A level 33 combat encounter (for only 4 PCs).
That's 7 combats, plus the skill challenges, and three of those combats are level +4 or above.
I don't have such good records for Heroic tier, and my memory isn't that reliable, but I suspect it tended not to push as hard as this.