What are these radial line patterns shown in representations of antarctica?
I can't be sure, but I strongly suspect that the radial lines in the first two images are the result of a bug in the software used to draw the map, probably resulting from vector polygons that are described in an inappropriate coordinate system going around, or too close to, the south pole.

It's impossible to guess at the meaning of the blue lines in the third image without any caption or context, but from referring back to your link for the article that you took it from, my guess would be that the lines show the tracks of the flights that gathered the data. 

No, they are not related to each other.