bbq island against retaining wall
Why does it have to be at a 45 degree angle? At the angle, you have a hole behind the counter where debris could get caught and become messy and a potential fire hazard. If you want the angle for aesthetic reasons, you should have a way to get back there and clean it out. As for the back side..that is up to you. If it won't be seen, then it won't matter. If you are worried about heat or something/someone getting inside it from behind, then use brick, stone, whatever. As for the floor under the oven area, pour extra concrete or use patio pavers. Its all about how it will look to you. I would also leave some room between the wall and island in case you need to repair either the island or the wall in the future.