Everything looks good.
Conway: your crossings are all negative and should be positive. (fixed)
Conway: the planar graph seems out of place in the conway notation section. (fixed, moved to its own section)
Signed planar graph: looks good. Move it up to the first section on names and notations. I think it fits well there. Also, pull a copy of graph out of the justification box so that it is visible without opening the box. (done)
Signed planar graph: change the name from planar graph to signed planar graph (fixed)