It's important to understand that cats have a very different psychology than dogs or humans do. Like us, dogs are pack animals. Co-operation and pleasing the pack leader are survival skills that work in our favour when we want to train them.
Cats, however, are mostly solitary hunters. They don't have the same instinct to please that dogs have. This does not mean that cats don't love their humans, but it does mean that they perceive relationships very differently than pack animals do.
Your cat is not dropping vases and cracking cups to be mean or even disobedient. Perhaps it's doing so because it's fun, or because those objects are in its way, or even just by accident. If you yell at the cat for doing these things, the cat won't understand that it has broken some rule. The most likely result is that the cat will become nervous, and perhaps break more things out of anxiety-induced clumsiness.
Preventing the cat from breaking vases and other ornaments that stay in one place is pretty easy. Get some blu-tack (or something similar); it's a substance that looks a bit like chewing gum, and can be used to stick things in place. Problem solved, and your ornaments are safe from earthquakes and clumsy humans as well!
Are there surfaces that you want the cat to stay off of? The best way to prevent a cat from doing something is to make it unappealing to the cat, but without frightening the cat. Many people keep a spray bottle of water handy, and when the cat jumps onto the forbidden shelf, it gets a squirt. This doesn't frighten the cat (who probably won't even associate the squirt with you) it just makes it associate something unpleasant with being on that shelf. There are lots of options here. Rather than a squirt bottle, I just clap when I want my cat to stop doing something. I only clap once, and not very loudly, just enough to startle but not frighten her.
As for fighting with the other cats, the squirt bottle can work well there also. Whenever a fight occurs, spray the combatants. But also make sure that there are lots of places where the cats can get away from each other when they want to be alone.
You'll find loads of other tips on this site for specific problems. Good luck!