1) Live rock is rock that is covered with the beneficial bacteria you will need for your tank.
2) You can provided it's big enough. It will need quite a bit of cleaning to make sure you don't see a build up of nitrates or any other element.
3) An RO
is recommended, as tap water will put in a large amount of algae causing elements into your tank.
Tap Water in the Saltwater Reef
4) I typically use aragonite sand in my tanks. You can find it in many different brands and varying grades from course to fine.
5) The same basic cycling principles will apply however it is a different type of bacteria than freashwater. You cannot seed a saltwater tank with fw
bacteria. However, the same basic methods to cycle will work.
Cycle your salt tank
6) That's the big question.
everyone has a brand they favor. You can try a few and find the one that works best for you. You could always give instant ocean a try.
7) The anemone will need a VERY high amount of lighting. We'll talk more about that nem in a moment.
8) It would be easier on you in the long run if you get a lion eating frozen foods. I've used live food to get lion to eat until we can get them eating frozen foods.
9) You don't need a special heater, just one that will keep the tank around 76-78
10) You shouldn't need to add anything really.
11) In my opinion your stocking won't work together. Over time that lionfish and the eel will eat the shrimp and nemo. I would go with either the aggressive fish or begin looking into a smaller, happier fish to go with the clowns and the nem.
As far as the nem goes, they typically need a very established tank with a large amount of lighting. That would be something to strive for in the future. Clowns do not need an anemone to be happy, nor is there any guarantee they will host it.
Hopefully that answered your questions.