I am having problem with the hotkeys for midpoint snap and angle constraint

Try a super simple example like this: 

Are you able to subdivide one edge, move it along the Y axis, and then snap that to the center of the edge in the back? Hold Ctrl if you don't currently have snapping enabled. 

For Edge Perpendicular, try the same test but moving the vertex along the Z axis. 

Yeah, the newer knife tool has a lot more snapping options and should make things easier overall though it may take a minute to get used to. Thanks for updating this thread!