The forums here are for Blender development. Questions and discussion about *using* Blender belong on blenderartists.org If your thread was moved here, you are probably in the wrong place.
not sure how you want it to look afterwards (especially the connected geometry), but you can try "To Sphere", you can then move mouse or enter a value between 0 and 1 (= 0 to 100%)
I'm sitting, waiting, wishing, building Blender in superstition...
I don't know that there is, though I can certainly think of cases where it would be useful. Assuming that there isn't already, if I had the skill set needed to do it, (and I don't yet), what I'd do is to write a script that would extrude from selected points, scaling them to a common center, and merging them together. Then I'd calculate the median of the lengths of the edges connecting the center and the selected points, and assign each edge that length keeping the center point fixed.
Now, I know how I'd do it if I knew enough about python, and the Blender internals to accomplish the task. Unfortunately, I lack the necessary knowledge and the necessary skills.
ns