In Modo you can make inactive Meshes either Wireframe or the same as the active Meshes. This usually involves going into the 3D Viewport Properties via the ‘o' key, you can assign a shortcut but what if you want a shortcut that toggles the behavior well you can do that too by using ‘?+‘ which is the toggle instruction for all boolean commands. So in the Map to shortcut dialog use this instead of the given TRUE or FALSE

If you want to remove an Edge and keep the vertex, you can use the UI button F2 Model Tab > Edge > Remove You can also use right-click the edge and select remove. It pops up a dialog box where you can check Keep Vertices Assign it to ALT Backspace for example to make it easier to access