I'd open it above like a 'pass-through' and bring the table out in front of it with a bench under the opening.

go to a lighting show room, take pictures of the space and any ideas you have. They are best suited to help you. also have a budget. the how to part is nice but most consumers have no idea that the pendants above are probably 300.00 each. Budget for lighting! take advantage of the pro's in the lighting world, its all we do!

If you love the marble tile, go for it! You can always buy a stainless or white range hood backsplash like this http://www.wayfair.com/Air-King-Range-Hood-Back-Splash-SP2430-AXK1174.html to slip in place when you are cooking something really messy. I have a travertine backsplash and use a stainless sheet when frying. It works great and no worries about stains ruining the stone.

pendant lights looks nice only if place above a table like a breakfast nook or island. hanging them freely does not complement their look. since there is no island under the ceiling try to embed recessed lights in the ceiling. alternatively track lights will also look great if you need brightness.