1- Can you number your questions? It saves on typing and we aren't paid by the word. Come to think of it we aren't paid at all.
2- Sometimes large chunks fall out, it turns to sand, there isn't anything behind the tile anymore, you interrupt your neighbors bath.
3- Standard thinset such as Versabond. Nothing less that $11/ bag. Dry powder that you mix with water.
4- See #2
5- 100% silicone is best all around the perimeter of the new dish, unless it sets flush with the rest of the tiles. In that case grout as usual.
6- Don't worry about the terminology. We'll fix that and you'll learn as you go.