A good tile installer that knows what he is doing, can easily remove that single piece of tile.... carefully replace it with another one. Do you have another extra pieces of the same tile? Do you know what brand and color the existing grout is? That will be more of the issue trying to get the grout match to match up or the finding the same tile (in the same dye lot) if you need to buy another tile. Did the heat cause the break or did a pan bang into the glass? Consider installing a heat resistant Lumicor or 3 Form panel behind the stove. Any flat material that can be sandwiched between two resin panels. 1). Crushed glass. 2). Fabric. 3). Fabric. 4). Fabric.

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.

I'd put in a tile backsplash. Stick with a solid color tile so your bottles won't get visually lost. Solid color doesn't have to be boring, look for interesting shapes or textures, and play around with different colors of grout to make a statement. The one in your picture looks very similar to the 2nd picture below.

Yes, ofcourse. Infact, they one of the best option as they are durable and easy to clean.