I think there are level 60 raids but people hardly ever go on them. I went on my first raid at level 70 (Black Temple). The pre-80 raids are novelties only and level 80s will run them to get the achievement. I think most of the pre-80 raids have requirements that you be "attuned" to the instance (usually through having enough good gear).
It used to be in TBC you needed attunement for even some of the Heroic or even getting into the first raid area (Kara). Now that dont need anymore.... or not as heavy.
There is 60 / 70 / 80 raids as per each "expansion" and yes 60/70 have been "degraded" to being novelties for achievements. But dont be mistaken by no means can you /faceroll on them. You need to pay atleast some attention even when you are level 80 and/or well geared 80.
Raiding in earnest will begin at level 80 after you've gotten enough gear (presumably via heroics) to last without dying quickly.
Getting gear is so easy now, what with Emblems of Triumph dropping free from the sky... You can get geared enough to go into Trail of the Crusader 10 or 25 man without ever seeing (in order of gear) Obsidium Sanctum, Naxx, Eye of Eternity or Ulduar
The first raid instance is Naxxramas which requires you have cold weather flying just to get into (unless you do a quest to get into the instance). Naxx is pretty difficult and requires a lot of coordination between party members to complete successfully (thus the use of Vent). Raids get more difficult after that.
We do raids without Vent most of the time, it takes some tries but it would to with Vent. I have had HORIBLE raids with Vent and GREAT raids without.
Vent does allow more easily for an "ok" raid to be lifted to success vs one without, that is PRESUMING people listen.
Naxx you dont require Flying though, you can be summoned in using the stone.
Ulduar is the place where you NEED flying, unless your group/raid has a warlock in it that can make a stone. The only stone there is "downstairs".
As far as a DK tank goes, I have a lot of bad BAAAAD experiences with damn ignorant full of them selves dk tanks... A LOT... A few very few good ones.
Tanking is a serious SERIOUS job that can go very wrong and spell major disaster for the raid team. A tank is the "pivot" of a raid, though 1 mistake can make disaster... it is usually DPS that "slip up" by taking to much damage or causing to much problems for the tank.
We in our guild have this rule:
Tank dies, Healer's fault
Healer dies, Tank's fault
DPS die, DPS Fault
And George, dont be fooled about holding agro to much. Agro is 2 things, the tank and the DPS. If my mage blasts away at 100% I can out agro most lvl 80'starting' tanks without problems. However if I am in UK with a starting tank he hold agro just fine, because I am only going at 50%.
Agro is a game of DPS, boss, adds and Tank, while the healers keep everyone on our side alive.
Tonight I should have my first 'real' raid in ICC

been there a couple of times with random groups but this is mostly my guild with some accosiated friends.
ICC Here I come !
PS. 2 level 80 chars myself, Holy priest to get a feel for the healing side and my main MAGE doing almost 8k dps in 25 man.