There are several companies which can print pictures on tile. This is fine for interior work but the kiln fired method is superior for outdoor use. If you have any particular photos or art, you can transmit images through email, ftp upload, or send pictures to be scanned. This allows wide flexibility for resizing to the installation of your choice and allowing photo editing.

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.

Mukti, From what you described, it seems you need a water softener than a hydrophobic coating. Salt based softeners are good for these issues.

You could go for tiles with design if they are simple ones. if you want plain, you can add some life in the country style with an exposed brick facade or subway tiles. for colours, it depends on how far out of your comfort zone you're willing to go. white is the safe choice, but you can go for blue, green, yellow, all pastel hues