Well, these are all very good questions, but the answers will vary widely based on your spec, your group composition and the encounter. I'll give you some general guidelines.
1. Combat Cycle. This is a term used to describe how Rogues use our CPs. For a Combat Sword Rogue, the cycle would be written as 2s/5r. this means you use SS until you get 2 CPs and use Slice and Dice. Afterwards, you SS until you have 5 CPs and Rupture. Rinse, lather, repeat. Once you get two pieces of T4 for the SnD bonus, that would change to 1s/5r. Combat Daggers will generally use 3s/5s/5r, or a slight variant.
2. Aggro management. In true raid situations, this generally isn't a problem. Idally, you should never feint, ever. It's a rather hefty energy cost for what little threat it does reduce (about 1k). Vanish should be used at around 70% boss health, or if you're getting too close to the tank before that and don't want to back off DPS because of an enrage timer (Gruul, for example). If you're having trouble getting to 70% before you Vanish, get a Pally to hit you with Salvation.
3. Cooldowns and Amps. Generally, you want to stack these for the greatest effect. Stacking haste effects multiplies, so if you get a few haste effects going, they'll multiply eachother, then adding other amps on top will scale more than normal because of the extra synergy with the stacked haste. When you use them will depend on the fight. You want to be able to use them as many times as possible. Getting a 5 minute cooldown off twice isn't uncommon. I generally pop my amps immediately after a Vanish so I can completely ignore my threat, and just focus on doing the most damage I can during this time. If you can communicate with your Shammy (if you have one) and get him/her to use Bloodlust with your amps as well, you'll be putting out some monster DPS.