I'm not sure what a space frame is, but edges alone aren't really usable, except as part of the creation of geometry. Graphics cards won't render edges, nor will any offline renderer that I know of. I know Blender has a modifier that turns edges into faces which is great for getting organic shapes, but it doesn't count for this because the end result is real quads, not just edges.

Blender itself can create vertices, and edges, and of course faces, without a restriction on them being attached to anything or being a part of anything. I would think that 3dsmax could too, but with all the different tools and buttons, it may not be as easy to do as in Blender unless you know the software(which I don't).

My recommendation though, assuming you actually want to render this in some form(game engine or other) is to create a thin cylinder. It can be as small as long as it is visible, and it will actually render if it has any size at all, and your camera can see it.

I don't know whether there's a way to start with an empty object, but you should be able to simply add a simple shape--a cube, for example--and then, in Edit Mode, simply delete all but one of the vertices. From there you should be able to add vertices by extruding from individual extant vertices, I believe.

OK, Blender should work for this, though I really would have thought that Max could do it too. Anyways....

The quickest way to get a single vert is like you already know. Just put some primitive and delete most of it. The typically used one is the plane as it only has 3 verts to delete.

For the mirror, you are looking for one of Blender's modifiers(the "mirror" modifier). On the right panel, see the long list of tabs in the middle/upper area. One has a wrench, and is the modifier tab. Use it to add a mirror modifier, and it will automatically mirror one side to the other, and this is in edit mode. The thing to watch out for generally is the clipping setting. It makes things on the middle axis stay right there. So you can't have anything cross that axis from one side to the other. This makes it really easy to things exactly on that edge, but once something hits it, it doesn't know which side it came from anymore so nothing can leave that edge either. This is OK though, because it is a quick check mark you can turn off, move the verts, and turn back on again, but if you don't know about it, it can get you because you move things around and using scaling you can easily accidently push something to that line.

Which brings me to a quick tip. Blender has a little feature called the 3d cursor. You can easily use it to control many things, one of the most commonly used (besides controlling where to add things at exactly) is to control the pivot point of transforms. If you are in edit mode, the default are for things to scale by the center point of whatever it is that is selected. This is fine and dandy right, but sometimes you are paying attention to the mirror, and want to scale verts around but with the whole object(or atleast the middle of the verts on both sides of the mirror) to be the pivot point. Just move the 3d cursor to that middle axis and in the footer menu of the 3d view, find the little spot for the pivot point and turn it to the 3d cursor, and now the scale will be better for that specific operation.