regarding your backsplash, depends on the conditions. I just redid out kitchen and when I removed the backsplash tile, i was able to remove most of the thinset and repair the drywall. You may have to cut it out and replace it entirely.
If you do repair, get it as smooth as possible, then seal and drywall where the paper came off with Guardz. Then use a fast-setting drywall compound to fill the bad areas if any rock broke out. Once skimmed smooth and dry, paint with Guardz again. Use a WHITE tile mastic for glass tile, as you can see through the tile, and regular mastic or thinset will not look good. Use a 3/16" v-notch trowl, making sure you don't leave visible ridges in the mastic after setting the tile. Be forwarned, cutting glass tile is an absolute BITCH. I did glass at our old house, and went with ceramic subway tile this time because of how much of a pain in the ass it was, and I'm not a novice DIYer.
