Regarding all life on Earth having a "common origin", I think the so-called Cambrian explosion is just the sort of evidence needed to discredit that idea.
Let's say "evolution is a powerful force and it works" (just for the sake of argument). So we find out that for 3.5 billion years Earth was pretty much static ~ simple single cell critters hither and yon building stromatolites and layers of iron and limestone ~ then, bingo, in a very small period of time all the current types of critters pop up ~ yet, all the simple single cell critters that'd always been around are still around ~ doing nothing special ~ apparantly not evolving into a "SECOND CAMBRIAN EXPLOSION" or a "THIRD CAMBRIAN EXPLOSION", and so on, which, if they could have done it once they could have done it over and over and over and over ~ but they appear to have not done that.
Stromatolites continue to grow. Limestone continues to pile up. Presumably some critter somewhere is depositing iron or some other dissolved ion in great layers that will in a billion years be noticed by someone.
I think the easiest solution to this problem is to simply posit that life may have a common origin BUT life on Earth obviously has its origins in diverse places, not all of them on Earth.
In Darwin's time the structure of the Universe was little known hence his selection of a "little Earth" origin scenario.