Hi and welcome to wonderland,
It's like a mad hatters tea party here ,loads of helpers steel free to ask anything you like (,just don't ask where i was last night because I don't remember)
No you don't need to have a protein skimmer .
Live rock is probably better when starting up a tank helps cycle ,
Yes cuc is as you have said .
Live sand is quicker to put fish into but bloody expensive than normal aquarium sand and gravel .
Live sand you just pour the whole bag in liquid as well no need to rinse it that's why it's called live sand ,
Other sand and gravel will need to be washed to get rid off all the dusty crap in it before you put it in the tank..
Time consuming but save you a lot of pennies.
Before you buy sand and gravel work out what you want to keep roughly this can effect wether you have sand or gravel..
Use ro water if you can , you can buy it already mixed with salt or buy you're own and mix the salt yourself.(I used to mix my own years ago save a bit of money )(buy it ready mixed now just because it's easier )
There you go quick guide to first setup
Obviously you need a tank and a heater and a filter