Hi Nitteo
Welcome to the life of having an empty bank account!
1. Why? Without it pictures can look flat, lifeless and lacking in the colours that can give underwater photos that wow factor: yellows and reds. You won't regret buying one. Or two. It makes a world of difference.
2. Manual, TTL etc? I have a DSLR and shoot manual. What you can use depends on a whole variety of technical factors relating to the camera, the housing and the strobe. Digital has complicated this. But manual is easy and simple, a good way to start and nothing to be afraid of - especially if you are using digital as you can see the results straightaway and adjust.
3. Are they specific to a camera? It all depends! Some might be. You really need to decide what camera you want and work from there.
4. ECO-friendly. I'm not sure diving is completely eco-friendly some times! (how do you turn a good diver into a bad one? Give him a camera). There is no doubt that fish are not delirious at flashes going off in front of them. Who is? You can usually see when your subject is getting more than a bit hacked off or spooked - and you can back off. After a while you can judge when to avoid going that far. How close depends on the nature and size of the fish - and its skittishness. Most will clear off fairly quickly when that strobes fires. Although a grouper having a doze under a rock might hang on for two or three pics if you are lucky.
I hope this helps a bit......
Tim