Draw a plane and then hit Spin Dup. See how you get a bunch of overlapping faces? This makes them a little hard to manage. Is there a way to “simplify” (something similar to removing double vertices) all these faces by joining them or something?

Its better to do the math first to ensure that they link properly - I often start with a circle of nodes as the no of faces I want (eg if I want a 90deg arc with 4 faces Im make a 16 node circle. I then edit one of the faces, delete all the others, place the cursor in the circle center and spin dup.

Any other approach is trial and error. If you have an arc of planes you can ‘simplify’ by selecting each pair of nodes from adjacent planes (ie bottom left on the left plane and bottom right on the right plane) and choose scale-0, that might get you to what you want depending on the complexity.

No, there isn’t any flatten image tool. All Blender really sees is the location of the vertices. Edges and faces are artefacts, so to speak, of verts. So, in order to have a connected up shape, you have to make sure the verts line up. If they do, then you can remove doubles.

You can make your two planes “one object” by joining them, but they’d still look the same. In order to “flatten” them into a single shape with the outline you want, you have to figure out a way to get verts at all the edge intersections. There’s no easy or automatic way to do that.