I'll offer some feedback but keep in mind I'm just an amateur photographer. I'm also constantly trying to take pictures with my iPhone 5 and make them look great. Your pictures are really nice and using the rule of thirds is great but remember it all depends on what you're shooting. The main aim of your pictures is to involve people in the picture, make it look great. So sometimes having it perfectly centered will make it look a lot better or having the main focus off to the side. I find personally that the iPhone is limited if you were to say compare the pictures to a DSLR so I try to take pictures that are really interesting to begin with and that sort of helps it transform from just snapshots to photography. Also for the limitations of the iPhone post processing can really help but that depends a lot of people view post processing as cheating for some reason. Anyway the more you shoot the better you get just while you're shooting look out for those really interesting shots that will really make things interesting. When you're shooting try to shoot things from different angles not just straight on so if you have to crouch or get up on something to shoot from a higher viewpoint.