Welcome to AA.
1. Idealy you would mix your saltwater in another container and have it ready to go. I use a big 55 gallon trash can on wheels from the local hardware store. Makes it easy to do water changes down the road. That way you can add the water in after the rock and sand. If you don't have/don't want to do that then i would mix the water in the tank first. Then add the rock and put the sand in last. You want the rock on the bottom glass so that your livestock doesn't move the sand out from under the rock down the road and cause it to become unstable. You can use a large diameter piece of pvc
to pour the sand down to the bottom of the tank in order to try and minimize the dust storm it will cause in the tank.
2. The penguin filter will get you started no problem. I wouldn't rely on that alone to provide flow in the tank though. SW
tanks need a bit more flow then fresh expecially if you plan on keeping coral. It is best to have some surface agitation to help oxygenate your water as well as break up the surface oils.
I assume by carbon rocks is the activated carbon filtering media. I would replace the activated carbon with some new media. Activated carbon can be used in both fresh and saltwater tanks.
3. Tap water ranges from less than ideal to really problimatic depending on the water in your area. It can contain phosphates/nitrates and a whole host of other undesirable chemicals and minerals. I highly recomment you avoid tap water if at all possible. If the supermarket water is the best you can find it will suffice. The best option which will pay for it's self both literaly and in avoiding all the problems that come with tap water is to buy a RO
unit. You can find them on ebay and several other online vendors for between 75-100$. This will make sure you know that your water is clean and pure.
Good luck with the new tank. Once you go salt you will never be able to go back.