First of all, mad props to you for asking questions and wanting to play the job properly instead of bitching about how its different from PLD/WAR. I will try to give you in-depth answers and not gloss over rules that have exceptions like I see a few other people commenting have done.
1. This is a mistake a lot of tanks make, is they will be too conservative with cooldowns and save them for an emergency situation that never happens. If you're not rotating cooldowns constantly, save for 1 or 2 that you're saving for a big hit, you're letting yourself take damage that could have been mitigated for no reason. In most content in the game thus far, you can save Shadowskin and/or Shadow Wall for any moderately powerful hit that you know is coming. If its *really* big, and physical, pop one of those with Dark Dance. If its *really* big and magical, pair them with a DA Dark Mind. Other than that, you can easily rotate Dark Dance along with things like Foresight and Awareness to level out and clip the claws so to speak, of consistent incoming damage from trash, boss autos, etc, because Dark Dance's recast time is so short. Work in Convalescence as well, and if you use Bloodbath, pop it when you have a lot of MP to burn on DA Souleaters and get some nice self-heals. If there is no tank buster worth saving a CD for, what I do is pop CDs in pairs, and when they wear off, pop another two. Use Shadowskin and Shadow Wall by themselves though. Your recast times are such that you should have minimal downtime. Always do whatever you can to mitigate damage, no matter how small. Tank busters are easy, countless guides will tell you what CDs to pop and when, yet everyone revolves their thinking around them and assumes that any form of mitigation or self-healing you have is only worth its weight only against a tank buster, which is extremely flawed, unbalanced thinking. Tank busters are a piece of cake to survive. Healers top you up, you push these two buttons, boom, done. Its the damage in between that can get away from you.
2. Its a pretty simple priority system. Get hate (hate is very easy to get and keep on DRK, in fact its a net loss to include it in our DPS rotation, so get a lot of hate and get it fast so you can start DPSing), keep Scourge up, keep Delirium up, if you're at greater than 75% MP you should be burning that MP on DA Souleaters. Even if there's a MNK in your group, if you need MP, Delirium is your top DPS. If you don't, DA Souleater is. If you're ever regenerating MP and you're over like 6K of it and you're not using it, that's bad. On that note, if you're off-tanking, don't pop Blood Weapon at the very beginning. The MP returns are wasted and thus you'll do a slightly better burst but you'll shoot your sustained DPS in the foot. Make a decent dent in your MP before you start popping CDs to regenerate it. It is hard to define a rotation for DRK because its all based on how much MP you have, so its very situational what you'll use. Aside from an opener, your sustained rotation is pretty much whatever the situation calls for, and keeping DoTs up. Also, the self-heal from DA Souleater is just fine. People like to say "if you're relying on X to do Y you've got problems" while describing a situation that is unlikely and silly. You use it consistently for steady, small amounts of healing, not to save your life from anything. As I said in the last question, avoid this mentality while tanking, where you focus on the buster and disregard maintaining your HP and mitigation in between, as if a tank's job entails nothing (other than hitting the boss) that isn't intended to survive a tank buster Boss autos are criting for 4.5K in Alex Savage, don't disregard the "fluff" damage, the devil is in the details, and in between the tank busters.
3. At the start of a pull, I'll get everything grouped up, pop a cooldown or two (unless there's mobs hitting me with magic I'll usually start with Shadowskin or Dark Dance+Foresight), pop Blood Price, and then immediately start spamming Abyssal Drain. During this I watch my HP. If I ever drop below like, 50%, that's when I'll DA an Abyssal Drain. However, it depends on how many mobs you have too. Abssyal Drain hits for anywhere from 3-550ish depending on your gear, so if you're tanking 4 or fewer mobs its probably a net loss to DA it. More than that though and you'll get like 2500+ HP from it. Basically if you're doing big manly pulls with 6+ mobs and you start plummeting it can be a good emergency button that will do damage, keep hate, and heal you for 2-4K depending on how much trash there is. If you drop below like 30% MP because a mob or two died really fast or wasn't hitting you much, switch to Unleashed. When Blood Price has about 1-2 seconds remaining, I stop AoEing. To sum up, I only do it if I'm tanking a LOT of mobs and my healer needs a little hand. And you should have plenty of attention to devote to that after popping your CDs and just standing there spamming one button
4. If you're tanking a boss and not a fuckton of adds, ALWAYS DA Carve and Spit. Watch its CD and make sure you're going to have the MP to do so. If you're tanking the aforementioned fuckton of adds, the 450 hit on only one of those adds is not worth the MP, you'd be better off (and doing more total DPS) using it to regenerate MP to continue AoEing. If you have to use it without DA on a boss, there is probably something you should have done different. On this note, its important to rotate your usage of DA based on its recast timer for maximum burst during times of high MP sustain. For example, you can time it so that you can DA two Souleater Combos and DA a Carve in between. One could argue that you can use un-DAed Carve to maintain MP to continue DAing Souleaters, but if you're DAing that many Souleaters in a row, you're almost certainly letting Delirium and Scourge fall off.
5. Never, unless I fuck up. Dark Passenger gains only 100 potency from DA, Souleater gains 140, Carve gains 350. So its a straight DPS loss. Weave in Passenger as often as you can and try and maintain MP to do so, but never DA it. Also, the blind is useless and actually a hindrance when you're trying to get hit by mobs to regain MP, so its not even really that useful when you're AoEing to DA it. It'd be a nice burst, but would neuter your sustain over the course of the pull.