Unless you're a professional photographer, your iPhone is likely the best camera you own. In fact, the iPhone is such a good camera, that it rewrites the rules for how to craft a professional video calling setup.
First sand everything down with 120 grid sandpaper.
For the larger gaps I would not use spot putty. Use a 2k putty instead. It is much harder and fills the lines better. You can also use a 2k epoxy putty like Miliput for this.
After filling, sand everything again with 120 grid. Then give it a 400 grid wet sanding.