Dodge now been removed from the game.
Dodge items do not stack additively. For example, Jax, with level 5 counterstrike, has 18% dodge chance. If he then picks up ninja tabi (+12% dodge) his total dodge chance is 28% (and not 30%).
It's easiest to simply calculate the highest %dodge first (as they stack multiplicatively, order is actually irrelevant): In our case, the 18% dodge chance from counterstrike is simply added (18% of 100% hit chance is 18%) so Jax's dodge chance is 18%, and his "be hit" chance is 82%. Next, the dodge chance from ninja tabi is added. 12% of 82% "be hit" chance is 9.8%, which then gets added to the previous 18%, for a grand total of ~28% dodge chance.
If there were another dodge item (say, an identical version of Ninja Tabi that stacked with itself), the +12% dodge would be 12% of 72%, or 8.6% increase.
The reason dodge is handled this way is such that the mitigation of dodge as a stat scales linearly; were dodge strictly additive, the more dodge% you had, the more damage further dodge% would reduce.
Ignite
Casting ignite on an already ignited target will reset the duration of the DoT, losing any remaining damage the original ignite would have done.
Speed
I'm just going to quote from the "mechanics FAQ" from the official LoL forum.
Q: How do movement modifiers work?
(Credit to Larias)
A: First, you have your base movement
of say 300. You add boots first,
always boots first, so if you have
boots added.
Let's say you get boots 2. That's 370
movement. Then, you get 35% movement
speed buff from items or runes or
masteries or buffs: that 370 is
multiplied by 1.35, or 499.5 movement
speed. If this is the only thing
affecting your movement speed, the
diminishing returns formula kicks in.
Now, let's say you get slowed by 38%
(ashe arrows). What happens is the
ORIGINAL 499.5 is multiplied by .62,
and you get 309.69 movement speed.
Because 309 is not above or below
diminishing returns, you stay at that
speed.
Q: What are these diminishing movement
returns? (Credit to Guinsoo)
A: For each point of movement you
would have above 490, that amount is
reduced by 50%. So if your final
movement speed was 748, it would be
reduced to 490 + (748-490)*0.5 = 604.
For each point of movement you would
have above 415, it is reduced by 20%.
So if your speed after all mods was
445, you would end with 415 + 30 * 0.8
= 439.
Q: Do slows stack?
A: Yes and no. Slows from items do not
stack among themselves (Phage, Frozen
Mallet, Rylai's Crystal Scepter).
However, all other slows stack.
Just like the diminishing returns for
bonus movement speed, being slowed has
diminishing returns starting at and
below 210.
And one addendum: The strongest slow/speed boost is always applied first.
Lifesteal
Lifesteal has no diminishing returns. If you hit an opponent for 20 damage, and manage 200% lifesteal, you will regain 40 health.
Lifesteal is based on damage done, so it is reduced by Armor (which does not have diminishing returns, see below) and doubled (or more!) by crits.
Attackspeed
+Attackspeed from items is additive and references the base attack speed of the champion. Buying two phantom dancers, for example, gives you 110% additional attacks per second, but because they are additive, the effect doesn't increase due to any other items you may have.
Attack speed has a hard cap of 2.5 attacks per second.
Armor and Magic Resistance
The effectiveness of Armor and Magic Resistance do not suffer from diminishing returns.
Please see this answer for a fully detailed explanation of why.
Here are the answers to this question(s) one-by-one:
What does [Pix's] damage scale from?
Pix's damage scales with Lulu's level. The formula for Pix's damage is:
Pix fires a barrage of 3 bolts, dealing 3 + (2 × level) magic damage each
Does it scale with AD, AP, etc.?
As you can see from the formula above. it does not scale with Attack damage (AD), Ability Powers (AP) or any other champion stat (Mana, Health, etc.) and is based solely on Lulu's level.
Is Pix's damage Magical or Physical?
Pix deals magic damage exclusively. Therefore his damage is dependent on the users Magic Penetration and the targets Magic Resist stats. There is some speculation about whose Magic Penetration Pix uses when making his attacks from an ally (not Lulu) as noted in this link.
Does Pix attack when the ally uses spells, or just for autoattacks?
Pix's attack is triggered by autoattacks only. Casting spells that refresh the attack animation (Nasus's Siphoning Strike, Blitz's Power Fist, etc) may provide additional attacks from Pix but to maximize the damage you probably want to target a champion with a higher attack speed.
For more information about Lulu and Pix check out her entry on the LoL Wikia.
Best Answer
I did a bit of research and apparently the stat shows all incoming damage that didn't directly affect your health bar.
This means basically every form of damage mitigation counts. (Blinds do not since they are a form of CC)
Some people on reddit are also complaining about shields from supports not counting towards the support's mitigated damage, but the target's.
For your example about Ezreal having 7000 damage mitigated on himself: Depending on the support he had, shields (Janna E,Morgana E,Bloodthirster) contribute to this stat but also items (Kight's Vow, Phantom Dancer) and spells (Exhaust, Urgot Passive).
However most of this mitigation will almost always come from resistances. Keep in mind that even a squishy marksman like Ezreal has at least 30-40 MR and 30-80 Armor. In addition to that most people run Armor and MR runes which results in quite a bit of mitigation, especially against bruisers or champions that haven't built any resistance penetration yet.
There are still three scenarios I'm not entirely sure about how they work: Stasis, Invulnerablity and Invincibilty.
DoT spells continue to tick if someone enters stasis, Tryndamere's ultimate simply doesn't let you die and Kayle's ultimate renders you completely immune to damage. I'll test these things and update the answer accordingly.