Notice: This post only applies to games up to HeartGold/SoulSilver. The EV system has changed since Black/White. For more details, see DragonLord's answer.
Technically, every 4 EVs gained will result in 1 extra stat at level 100. For example, if you took two level 100 Snorlax, with identical natures and IVs, but one had 4 EVs in Attack and the other had 0 EVs in Attack, the former would have 1 more point in its Attack stat than the latter.
The EV-effected stats gained during level-up don't all happen all at once. DisgruntledGoat described what occurs in a good way:
On level up, the game will calculate how much of a stat point increase you would have at that level and adds it on. For example, if you have a level 50 Gyarados and you earn 200 EVs (50 stat points), you won't get +1 extra point per level up. Instead, you'll get around +25 on the first level up (because at lv50 you would have earned about half the points), then +1 for roughly every two levels after that.
Of course, if your Gyarados was level 99, had cleared EVs, and then you battled all those low level Pokémon, you would probably see a very large stat boost from 99 to 100.
Your Trainer ID and Secret ID is generated by the seed that is randomly generated when you start the game for the very first time. It is not defined by your name or gender. There is no possible way to change your IDs without restarting completely or using a save editor or cheating device.
In Generations III, VI and V, your Trainer ID and Secret ID is used in conujunction with a Pokemon's personality to determine shininess. There is a 1/8192 chance of getting a shiny Pokemon.
First, your Trainer ID and Secret ID are XOR-ed (Exclusive OR - one or the other but not both, Ex. 11010111 xor 01101010 = 10111101). That result is saved as variable E.
Then, the encountered Pokemon's two personality values are XOR-ed, with the result saved to variable F.
Finally, E and F are XOR-ed one last time, then checked to see if the final result is less than 8. If so, your encountered Pokemon is shiny.
Here is an example on Bulbapedia, which includes all integer to binary translations.
Best Answer
Off the top of my head:
These abilities activate when the Pokemon is in the first spot of the party:
Most if not all of the above abilities are still active even when the Pokemon is fainted.
These Abilities will activate regardless of their position in the party:
In generations past:
Source for the ones I missed originally: