Yes, the cycle is the same in SW.

Live rock serves as a host for the bacteria, and while tufa and other rocks will host the bacteria, the other organisms must be introduced into the tank. This is why buying live rock is a good idea, even if you only get a few small pieces--they'll introduce the organisms, which will then spread to other 'base' rock you put in. The rock also provides a great hiding place for the fish and such to hide--great, natural habitat!
Cycling can be done with either ammonia, or adding raw cocktail shrimp, then monitoring--as with FW, you can use the ammonia to better control the levels.
The skimmer can be run in a sump, or you can try running it over the edge--it just depends. I'm not that familiar with most of the brands, so you'll have to check with someone else for specifics. They do all need a pump or powerhead to run them, but the size pumps needed will vary with the skimmer.
Your water actually looks pretty good--really low nitrates, so the water changes won't be contributing to what the tank produces overly much, and there don't seem to be high levels of copper, or sulfides. The test doesn't list phosphates? Or silica--and while those things can be a concern, they aren't insurmountable. Lots of people will tell you that you MUST use RO/DI, but I've always ran my tanks using water that was filtered for sediment and heavy metals, but not for anything else. Treating for chlorine/chloramines would be necessary, as well.
Other equipment: Lighting, as you know. A few powerheads for water movement. It's more important in SW than FW, IMO--many FW tanks run with just a filter for water movement, and that really won't work in a SW setup. And, there is equipment that you don't need--SW tanks, with adequate live rock and such, can be run without any power filters or canisters. The bacteria will colonize the rocks and sand, and a power filter can act as a nitrate trap, holding solid wastes that decay and spike the nitrates as they're broken down.