I understand how to get the white splatter dots, but what do you suggest is the best way to get the buttercream with the blue and white mix as shown in the inspiration pictures below? 

Thank you! 

The picture didn't come through.

I see the pic Freckles  -- try reloading :)    My suggestion is to take some of the blue icing and lightly mix in some white.  I'd do just a little at a time until yoiu are saisfied w/the results.    You also might try just  lightly smearing a very small amount of white over the blue rather than mixing it.  Just put a very thin layer of white on an off-set spatula and smear if over the blue.  Anyhoooo that's what I'd try.

Thanks kakeladi, I was thinking the second one that you mentioned but wasn't sure. I will practice and play around with that option. 

This tutorial only shows how to do the sides, but you might still find it helpful. Her method is similar to Kakeladi's suggestion, but she makes a point of saying to smooth the splotches of color clockwise once, and then again counterclockwise to get better results

The top of the cake appears to be either airbrushed or dry brushed with petal/luster dust, to me.

Thanks for posting the tutorial angesradieux! It was really helpful