There is a nice, old, script floating around to help you out. Google planarize or similar.

Faces with holes that has no splits can also be impossible to split. Triangulating the face and then delete the extra edges is a simple remedy.

You can't have a curve that is both per se. One solution is to have multiple CVs at the corners to make the corner straight. Let Maya do it for you using combine. Try the different options to let it...