In Maya, if you are editing a curve and have a point selected, you can press arrow up or down to walk your points. If you have a point selected, and you hit the right arrow, you now have the point to the right of your original point selected. I tried googling it but only came up with the vex command “neighbor”. Thanks!

No, I don't believe this feature exists. Feel free to submit an RFE.

I'm curious, in Maya, how do the directions map if there are not exactly 4 neighbors to a point? How do cardinal directions ('right', ‘left’, etc) correspond to topological space, is it always relative to the current view (screen space)?