Throwing the dead shrimp in the tank will make live rock and live sand from the base rock and sand you put in. For filtration terms, "live" means that it is packed with bacteria that will grow from eating the waste of the rotting shrimp. Decorative "live rock" is another story and will require you add at least 1 piece of rock that has actual sea life growing on it.
If your rock is already cured, than I would wait before introducing it to the tank to prevent more die off. If the rock is uncured, I'd add it now and let it cycle your tank with the die-off.
You can rinse the sand before you add it or you can choose not to. If you don't rinse it, you will be a little cloudier for a little longer, but either way it will eventually settle down. Rinsiing a few hundred pounds of sand isn't nearly as fun as it sounds in my experience.
Once you have the water mixed and in the tank with the sand/rock, you can add the shrimp. The cycle will take about 30 days,(ballpark), maybe less, maybe more. There is no need to be in a giant rush in this hobby. The only things that happen fast in SW
are bad things. The good stuff takes time, so don't be in a hurry.