I know what this strategy for farming exp. is, but I don't quite understand it.
Why can't you just auto-attack a minion to get it's health down lower? Wouldn't it take longer for it to die if it is just your minions fighting it?
Thanks.

Minion control, so that your minions will stay closer to your tower, giving you more protection/.

The point is actually to prolong the life of the opponent's minions when farming. The closer you are to your tower, the less likely you are to die. If you kill all the minions in the way, then the only way to farm is by walking away from the tower, meaning you are more likely to be ganked by the jungler, champions with teleport abilities, or roaming pushers.

pushing the wave by straight autoattacking creeps low then last hit it leaves your lane wide open to ganks

when you aren't even level 30 who cares but after lvl 30 people get more serious about their lanes since no one likes being ganked every 2min

last hit gives you gold, keeping their minions closer to your side of the river keeps you alive.

Sometimes it's actually smart to push your lane like mad. If you know their jungler won't have a strong gank, or you have wards, you can push the lane to your enemy's tower. That way they'll have a harder time farming and will fall behind in creep score. Only do this if you're sure you'll survive ganks without having to do something drastic like waste flash.

Last hitting minions is always important level 30 or not. Its only less important with no junglers.

There are two reasons for last hitting.

The first and most important reason is to get more gold. If you auto-attack, you'll often lose last-hits to minions that randomly land the killing blow in between your attacks. With a bit of practice you'll be able to get a lot more gold by last-hitting, especially early in the game.

The secondary reason is for lane control - any damage you deal pushes your minion wave forwards, which makes you more vulnerable to being ganked.

Lane control is actually a surprisingly deep concept Check out http://www.youtube.com/watch?v=tj2l3ilS2Fo as an example of how far it can go.

Note: You should generally last-hit, but sometimes you should push hard instead (to get the tower, or to buy time to go b, gank another lane, protect a tower, get map objectives etc). There are relatively few times that you'd just auto-attack (maybe if you needed to conserve mana?).