How is sushi supposed to be eaten?
Clean your hands before you eat. Often, you will be given a hot towel for the purpose. Return the towel to the server neatly folded.

It is fine to eat sushi with your hand, as long as there is rice with each piece of fish. Sashimi (sliced fish not prepared with rice) should only be eaten with chopsticks.

If you sit at the sushi bar, feel free to converse with the itamae (sushi chef) if he's not too busy, and to order sushi from him. Do not order anything but sushi from him, order non-sushi items from your server. It is classy to ask the itamae to recommend a sushi item or even to ask him to surprise you. If there is something you know you don't like (uni is mine), let him know because it is very rude to not clean your plate. By that I mean don't even leave a grain of rice.

Mixing wasabi with the soy sauce is so common that you can get away with it, but it is considered kind of tacky, at least in a fine restaurant. So is eating ginger with a bite of sushi. You're correct that it is intended as a palate cleanser between sushi 'courses'. Again, if you want to, you're not going to get kicked out for it. In fine sushi restaurants, sushi is often not served with wasabi on the side. After all, the chef is an expert, he knows more about sushi than you! And presumably he knows how much wasabi should go on each piece of sushi. If you really want more, go ahead and add it if it's there, or let the itamae know your preferences in the matter.

Regarding dipping into the soy, try not to soak the rice of nigiri-zushi (shaped rice with a slice of fish on top). Just lightly dip the fish. Ideally, place the bite into your mouth fish down. Try to eat the whole piece in one bite. If you must, bite it in half but don't put the second half back on the plate. It's funny, but the video in @Mel's comment to the question shows tossing a big piece of sushi down pretty well :) Just know that the dunking it in soy sauce is a joke!

If you are in a part of the word where tipping is expected, tip the server and itamae separately. Often there will be a jar on the bar for tipping the chef. He would rather not touch money while he is working.

You can offer the itamae a sake if you're so inclined. 

Finally, leave your chopsticks laying across the soya bowl between uses, or on the holder if there is one. Never leave them on your plate or (heaven forbid) sticking out of your rice. 

Regarding your edit, not necessarily. It is completely optional to use chopsticks to eat rolls or nigiri. It is entirely up to you. It's like using the provided spoon to eat the usually provided miso soup. Drinking it from the bowl is totally acceptable.